Definitely feed him if he is hungry. My son was also VERY large. He weighed a little more than yours does at this age and was slightly shorter, so he was "chunky". The doctor's didn't like the fact that he was in the 95% on the chart, but he followed the curve just like he was supposed to. He is now five and the tallest boy in his class and he is not chunky at all. But, he definitely can go through eating spurts where he eats more than the adults do.
I think the key is sticking to healthy foods. Another food NOT allowed now is peanut butter. Don't put it on break or crackers for him yet. For healthy finger foods, I like carrots. Plus, if you chop a sweet potatoe and then steam it in the microwave, the pieces hold their shape and are also good finger foods.