When do they start to classify kids as overweight?

We have a 2yo (26m to be exact) who is obsessed with food. We never did purées, and from the day he picked up a whole broccoli floret and shoved it in his mouth, he’s been gobbling up almost anything we put in front of him. Great right? Except 90% of his meltdowns at home are food related, and at his 2yo checkup his height had slowed from maybe 75% to 50%, while his weight stayed in the 80%. Our dr didn’t say anything about the weight, just that we’d watch the height to make sure it didn’t keep dropping for any reason. But afterwards I checked a kids bmi calculator and it says he’s in the overweight category.

Up to now we’ve let him decide how much food he eats, and he almost always eats what we eat, so it’s not like he’s eating fast food every day - we cook dinner 5 nights of the week, his daycare has a chef on site who cooks their meals every day, he eats weet bix or yogurt for breakfast. I guess I’m just confused about whether we need to do anything about his weight, or whether we still let him set the pace for eating. The other night he finished 2 whole corn cobs, on top of his portion of steak and had a bite of broccoli. There was a little butter on the corn but not heaps. Should we have limited him to just one? We do limit snacks, but if he’s still hungry and wants an apple/pear/banana, he can have that unless it’s too close to mealtime. And if there’s something like mashed potatoes and he’s not eating the rest of his meal, we say no more of that but there’s chicken/fish/whatever else he’s welcome to eat if he’s still hungry. I know how hard it is to get back on track if you’re an overweight kid, and his seeming obsession with food has us doubting if we should be doing something differently.