how much influence the bull has depends which of his genes are dominant and recessive as compared to the cow. Nutrition plays a little bit of a role but it is more often that the cow is just overfed and is fat and has a hard time calving.
I believe the bull is 50% of the calf, so the bull has a 50% influence on the size of the calf. Nutrition in my opinion has a huge influence on the calf as well. If the cow is in bad shape, as will be the calf, skinny and unhealthy. Good nutrition means a healthier calf, therefore it will be heavier.