These are some of the reasons why Balarāma is known as Saṅkarṣaṇa, Balarāma or sometimes Rāma. In the mahā-mantra—Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare—people sometimes object when Rāma is accepted as Balarāma. But although devotees of Lord Rāma may object, they should know that there is no difference between Balarāma and Lord Rāma. Here Śrīmad-Bhāgavatam clearly states that Balarāma is also known as Rāma (rāmeti). Therefore, it is not artificial for us to speak of Lord Balarāma as Lord Rāma. Jayadeva Gosvāmī also speaks of three Rāmas: Paraśurāma, Raghupati Rāma and Balarāma. All of them are Rāmas.
(Srimad Bhagavatam-----10:2:13-----purport).

One day, Vasudeva sent for Gargamuni, the family priest of the yadu-vaṁśa, and thus Gargamuni went to the house of Nanda Mahārāja, who received him very well and requested him to give names to Kṛṣṇa and Balarāma. Gargamuni, of course, reminded Nanda Mahārāja that Kaṁsa was looking for the son of Devakī and said that if he performed the ceremony very gorgeously, the ceremony would come to the notice of Kaṁsa, who would then suspect that Kṛṣṇa was the son of Devakī. Nanda Mahārāja therefore requested Gargamuni to perform this ceremony without anyone's knowledge, and Gargamuni did so. Because Balarāma, the son of Rohiṇī, increases the transcendental bliss of others, His name is Rāma, and because of His extraordinary strength, He is called Baladeva.
(Srimad Bhagavatam-----10:8-----summary).

Baladeva was actually the son of Devakī, but He was transferred from Devakī's womb to that of Rohiṇī. This fact was not disclosed. According to a statement in the Hari-vaṁśa:
pratyuvāca tato rāmaḥ
sarvāṁs tān abhitaḥ sthitān
yādaveṣv api sarveṣu
bhavanto mama vallabhāḥ
Gargamuni did disclose to Nanda Mahārāja that Balarāma would be known as Saṅkarṣaṇa because of uniting two families—the yadu-vaṁśa and the vaṁśa of Nanda Mahārāja—one of which was known as kṣatriya and the other as vaiśya. Both families had the same original forefather, the only difference being that Nanda Mahārāja was born of a vaiśya wife whereas Vasudeva was born of a kṣatriya wife. Later, Nanda Mahārāja married a vaiśya wife, and Vasudeva married a kṣatriya wife. So although the families of Nanda Mahārāja and Vasudeva both came from the same father, they were divided as kṣatriya and vaiśya. Now Baladeva united them, and therefore He was known as Saṅkarṣaṇa.
(Srimad Bhagavatam-----10:8:12-----purport).

Mahā-Viṣṇu is actually an expansion of Balarāma, who is Kṛṣṇa's first expansion and, in the Vṛndāvana pastimes, His brother. In the mahā-mantra—Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare—the word "Rāma" refers to Balarāma. Since Lord Nityānanda is Balarāma, "Rāma" also refers to Lord Nityānanda. Thus Hare Kṛṣṇa, Hare Rāma addresses not only Kṛṣṇa and Balarāma but Lord Caitanya and Lord Nityānanda as well.
(Sri Caitanya Caritamrta-----introduction).

The Lord is advaita, without differentiation. There is no difference between the forms of Kṛṣṇa, Rāma, Nārāyaṇa and Viṣṇu. All of Them are one. Sometimes foolish people ask whether when we chant "Rāma" in the Hare Kṛṣṇa mantra we refer to Lord Rāmacandra or Lord Balarāma. If a devotee says that the name Rāma in the Hare Kṛṣṇa mahā-mantra refers to Balarāma, a foolish person may become angry because to him the name Rāma refers to Lord Rāmacandra. Actually there is no difference between Balarāma and Lord Rāma. It does not matter whether one refers to Balarāma or to Lord Rāmacandra when chanting Hare Rāma, for there is no difference between Them. However, it is offensive to think that Balarāma is superior to Lord Rāmacandra or vice versa. Neophyte devotees do not understand this śāstric conclusion, and consequently they unnecessarily create an offensive situation.
(Sri Caitanya Caritamrta-----2:9:155-----purport).

Śrī Caitanya Mahāprabhu personally renovated Vṛndāvana-dhāma and advised His chief disciples, Rūpa and Sanātana, to develop it and open it to attract the spiritual vision of the general populace. At present there are about five thousand temples in Vṛndāvana, and still our society, the International Society for Krishna Consciousness, is constructing a huge, magnificent temple for the worship of Lord Kṛṣṇa and Lord Balarāma, along with Rādhā-Kṛṣṇa and Guru-Gaurāṅga. Since there is no prominent Kṛṣṇa-Balarāma temple in Vṛndāvana, we are attempting to construct one so that people will be attracted to Kṛṣṇa-Balarāma, or Nitāi-Gauracandra. Vrajendra-nandana yei, śacī suta haila sei. Narottama dāsa Ṭhākura says that Balarāma and the son of Mahārāja Nanda have advented Themselves as Gaura-Nitāi. To propagate this fundamental principle, we are establishing a Kṛṣṇa-Balarāmatemple to broadcast to the world that worship of Gaura-Nitāi is the same as worship of Kṛṣṇa-Balarāma.
(Sri Caitanya Caritamrta-----2:16:281-----purport).

Although it is very difficult to enter into the Rādhā-Kṛṣṇa pastimes, most of the devotees of Vṛndāvana are attracted to the rādhā-kṛṣṇa-līlā. However, since Nitāi-Gauracandra are direct incarnations of Balarāma and Kṛṣṇa, we can be directly in touch with Lord Balarāma and Lord Kṛṣṇa through Śrī Caitanya Mahāprabhu and Nityānanda Prabhu. Those who are highly elevated in Kṛṣṇa consciousness can enter into the pastimes of Rādhā-Kṛṣṇa through the mercy of Śrī Caitanya Mahāprabhu. It is said, śrī-kṛṣṇa-caitanya rādhā-kṛṣṇa nahe anya: "Śrī Kṛṣṇa Caitanya Mahāprabhu is a combination of Rādhā and Kṛṣṇa."
(Sri Caitanya Caritamrta-----2:16:281-----purport).

In the Upaniṣads it is stated, nāyam ātmā bala-hīnena labhyaḥ. The purport is that one cannot attain the supreme platform of self-realization without being sufficiently favored by Balarāma. Bala does not mean physical strength. No one can attain spiritual perfection by physical strength. One must have the spiritual strength which is infused by Balarāma, or Saṅkarṣaṇa. Ananta, or Śeṣa, is the source of the power which sustains all the planets in their different positions. Materially this sustaining power is known as the law of gravitation, but actually it is a display of the potency of Saṅkarṣaṇa. Balarāma, or Saṅkarṣaṇa, is the source of spiritual power, or the original spiritual master. Therefore Lord Nityānanda Prabhu, who is also the incarnation of Balarāma, is the original spiritual master. And the spiritual master is the representative of Balarāma, the form of the Supreme Personality of Godhead who supplies spiritual strength. In the Caitanya-caritāmṛta it is confirmed that the spiritual master is the manifestation of the mercy of Kṛṣṇa.
(Krsna Book).

When Garga Muni was so eagerly requested by Nanda Mahārāja, he performed the name-giving ceremony as secretly as possible in the cowshed of Nanda Mahārāja. He informed Nanda Mahārāja that the son of Rohiṇī would be very pleasing to His family members and relatives and therefore would be called Rāma. In the future He would be extraordinarily strong and therefore would be called Baladeva. Garga Muni said further, "Because your family and the family of the Yadus are so intimately connected and attracted, His name will also be Saṅkarṣaṇa." This means that Garga Muni awarded three names to the son of Rohiṇī—namely Balarāma, Saṅkarṣaṇa and Baladeva. But he carefully did not disclose the fact that Balarāma had also appeared in the womb of Devakī and was subsequently transferred to the womb of Rohiṇī. Kṛṣṇa and Balarāma are real brothers, being originally sons of Devakī.
(Krsna Book).

A short time after this incident, both Balarāma and Kṛṣṇa began to crawl on Their hands and knees. When They were crawling like that, They pleased Their mothers. The bells tied to Their waist and ankles sounded fascinating, and They would move around very pleasingly. Sometimes, just like ordinary children, They would be frightened by others and would immediately hurry to Their mothers for protection.
(Krsna Book).