Why are antibiotics used on farms?

They are used as a growth enhancer at the subtherapeutic level--that is, at lower doses than you would use to treat an infection. Low doses are particularly good at selecting for resistant strains.

What I mean is that heavy doses kill off all the bacteria, including those that have developed weak resistance. In contrast, subtherapeutic doses may not be strong enough to kill off the weakly resistant ones, opening up the opportunity for further evolutionary changes and gene exchange.