Why rear wheels of a tractor are bigger than front wheels?

I think due to better grip when drum brakes are applied and to make rear portion a little heavier for balancing purpose

This thread is over 6 months old, but I'll play along.

Traction. Large diameter tires are better able to drive through ruts and mud without getting stuck.

So if large sized tires are better able to drive through mud then why is the front tire smaller in size than the rear one??
According to your answer the both tires can be same only to avoid stucking in mud?

The rear tires are the traction tires - the engine drives the rear tires and being large gives them more traction which reduces the rusk of spinning and digging themselves into a hole. The front tires don't provide traction, just steering, and so don't spin and hence won't dig themselves a hole. Plus the front tires being small gives the tractor a tighter turning radius than if they were large.