Obesity stats in Japan are aggregated across Japan not just Tokyo. It's true that outside of Tokyo, most of Japan drives, and is a lot less transit centric. But it's also true that most Japanese cities and towns are smaller and there's a larger culture of walking to a corner store, the local grocery store, the drugstore, a soba-ya, the shrine, the park, or other places, unless you're out in the boonies. And adults often move to Tokyo for work which means they stay fit until they become old enough to move back to the burbs to have kids. It's also very common for rural Japanese to walk along the side of the road to get places and get picked up by a friend/family with a car if the bus is taking forever to take them back.
I agree too many non-Japanese who just visit judge the whole country by Tokyo which is a mistake. But there's a much bigger culture of walking and standing in Japan than there is in the US. Heck, the US has a culture of parking as close to the store/restaurant as possible in the parking lot of any commercial area to minimize walking. It's hard to beat culture. Of course Japan is also a culture where obesity is a lot more frowned upon, the doctors chastise you much harder for it, and as a collective society people feel much more pressured to stay skinny. Japanese also eat much smaller portions and find that acceptable. And Japanese in rural, more car centric, areas often are heavier than urban Japanese.
I really don't think the small lot sizes are causal for Japanese not having kids, rather I think it's the other way around. Fewer folks in urban areas are having kids, dropping demand for anything larger than a 2LDK, so the market is responding in kind.