If it was sedentary lifestyles and plentiful food alone that caused the obesity epidemic, then it should have taken off in the 1950's.
Instead it took until the late 80s and 90s to really become a problem.
One hypothesis is that a virus spread throughout the population in 1980s-90s that perhaps was ignored because the immediate effects were either limited or similar to common cold/flu viruses.
Yet, this virus was different enough that it caused inflammation/immune response that led directly to obesity or subtle behavioral changes that eventually manifested itself as obesity.
I don’t remember a lot of sedentary lifestyles in the 50s at all. At least in the blue collar ranks, everybody was working pretty hard.
Of course darn near everyone smoked, maybe the nicotine kept everybody slim?