My son just turned 12 months, and he's 31 inches and 27 pounds. I let him eat what he wants when he's hungry.
My nephew is 9 months old, and is about 30 inches and well over 35 pounds. His brother and sister were both "big" - very big - until they were nearly 18 months old. Then they just shot up and slimmed down.
My oldest son was also "big" at 12 months, and grew out of it as soon as he started running more around 15-18 months.
Depriving children at a very young age of food when they are hungry can lead to very bad habits later in life. Both my daughters are adopted and were malnourished through the first years of their lives. They both "hide" and "sneak" food into their rooms, and eat voraciously when given a chance. One has a weight problem, the other fights it constantly. Despite the ready availability of food for both girls, they still have an almost instinctual need to hoard food - probably because they were deprived in their developing years.
Given that it's winter out and at this age (12-13 months) it's not easy for them to "go outside" and run/play, they aren't going to be nearly as active, so they aren't going to work off the food they are eating and they're going to store some up. I wouldn't worry about it at all at this age. If he's hungry, feed him. He may be growing through a growth spurt or he just may be growing faster than most children.
Try to instill good eating habits now, no matter how much he's eating, and he'll even out his eating/growth eventually. I don't think it would be a problem until he's quite a bit older. It's very hard for children to overeat at this age. They eat when they're hungry and won't when they aren't. They know what they need and when.
Society's obsession with anorexic body shapes right now is dangerous for young children. A chunky/hefty/stocky baby is a healthy baby. That's why they call it "baby fat". It will melt off when he's older and more active. I worry more about my granddaughter, who is so thin she looks ill sometimes, than I do about my "chunky" happy son.