We ate big meals, but we didn't eat anything else. When I see families now, they stock up with super mega sized snack food at Costco and cram it in their minivan (the 2 reasons for having a minivan being to drive soccer teams around and to take your super mega sized snack food home </snark>) When I was a kid, people didn't buy stuff at that scale. Homes were smaller too, as were refrigerators. You just couldn't do that kind of thing easily.
Of course, my excuse for getting fat these days is because I live in Japan and there is nowhere in Japan that isn't walking distance from a convenience store... That and my wife believes that beer has no calories -- a misunderstanding that I'm loathe to correct.
I don't know about your parents, but when I look at what was done for free time when my grandparents(born ~1930s) and my parents (born in the 1950s) did in their free time vs what my friends and I did I can't help but see a significant difference in the time spent active. I'm not just talking about going out to ride a bike/play basketball with my friends, but later in life. When my grandfather went to work, school, and even to a bar he always walked and my father had a similar relationship with mobility during his early to teen years. Of course that changed when they both were old enough to own a car, but for both of them that wasn't until they're late teens.
Combine that with the only entertainment being other places or outside you have a populace who expends significantly more calories every day than my generation (Millenial).
As time progresses I think you might see parents from the earlier generations feeding their kids at the level they were fed as kids not recognizing that little Billy watches youtube for 3 hours after finishing his homework instead of going and playing basketball with Tuk-Tuk leading to a daily calorie surplus. Over time a daily intake of +200 calories can easily add up to a significant amount of weight.
I don't have any data to support this other than my anecdotal story and how I approached weight loss (by decreasing intake and increasing passive/everyday calory burn rate), but I think it'd be a cool thing to see studied.