Balarama did not always favor Duryodhana. It is explained in Vana Parva SECTION CXIX that Balarama favored Yudhishthira.
Then Valarama, resembling in hue the milk of the cow and the Kunda flower and the moon and the silver and the lotus root and who wore a wreath made of wild flowers and who had the ploughshare for his arms, spake to the lotuseyed one, saying, 'O Krishna, I do not see that the practice of virtue leads to any good or that unrighteous practices can cause evil, since the magnanimous Yudhishthira is in this miserable state, with matted hair, a resident of the wood, and for his garment wearing the bark of trees. And Duryodhana is now ruling the earth, and the ground doth not yet swallow him up.
He even reprimanded Bhishma, Dronacharya, and Kripacharya and Dhritarashtra.
How is it that Bhishma and Kripa and the Brahmana Drona and the aged king, the senior member of the house, are living happily, after having banished the sons of Pritha? Fie upon the vicious-minded leaders of Bharata's race! What will that sinner, the chieftain of the earth, say to the departed forefathers of his race, when the wretch will meet them in the world to come? Having hurled from the throne his in-offensive sons, will he be able to declare that he had treated them in a blameless way? He doth not now see with his mind's eye how he hath become so sightless, and on account of what act he hath grown blind among the kings of this entire earth.
Another example of how Balarama supported Yudhishthira.
And the son of the god of virtue,--virtue which stands at the head of all the there pursuits of life--and the son of the wind-god and also the son of the lord of celestials, and those two sons of the celestial physicians,--being the sons of all those gods and always accustomed to a life of happiness, how are they living in this wood, deprived of all comforts? When the son of Virtue met with defeat, and when his wife, his brothers, his followers, and himself were all driven forth, and Duryodhana began to flourish, why did not the earth subside with all its hills?"