1. As another commenter posted, total calories consumed per capita has gone up considerably since 1970.
2. As you posted, we move a lot less than we used to. There are tons of studies that confirm this across a number of different metrics (e.g. average grip strength has gone down considerably since the 80s, https://www.npr.org/sections/health-shots/2016/06/13/4815909... ).
We eat a lot more, of more foods that have higher calorie-to-nutrient ratios than we used to, and we move a heck of a lot less.
Exercise does have many positive metabolic and other benefits, but not anywhere enough to be a causal explanation on its own. If people started walking 5 miles a day, every day, not only would there still almost certainly be a widespread and growing obesity epidemic, but there's even an argument that it could be worse. Increases in activity tend to drive increases in hunger which will typically surpass caloric deficits if somebody is not actively controlling their diet, in which case they would not be fat in the first place.
This is made even worse by misleading advertising which will do things like showing fit athletes drinking Gatorade, Coke, etc during their training or competition. And somebody goes and does a couple of miles on a training bike and does the same thing - which is going to send their net caloric input skyrocketing.
> Increases in activity tend to drive increases in hunger As far as I know, certain types of high intensity exercise do so but not necessarily all exercise.
If we take your numbers at face value, that'd be a delta of 684 pounds per 20 years. Again kind of an obvious indicator why these long term calorie/pound measurements are pretty dubious, but at the same time also an indicator of why diet is just so much more important than exercise for weight management.
[1] - https://www.pewresearch.org/short-reads/2016/12/13/whats-on-...
People who stop doing sports suddenly gain weight. People who get into sports habit like running or swimming slowly loose weight.
So, imo, this uber simplified model of just don't work like that.
Presuming one does not replace the burned calories, even walking 5km a day will burn the calorie equivalent of about 80 pounds of fat over the course of a year. It adds up. Conversely, not walking 5km a day adds up. After suffering a broken leg I spent a couple years largely sedentery in my late 30s, and I put on 25 pounds in that time. I snapped out of my stupor, started exercising again, and burned it off in short order.
"In 1969, 48 percent of children 5 to 14 years of age usually walked or bicycled to school (The National Center for Safe Routes to School, 2011). In 2009, 13 percent of children 5 to 14 years of age usually walked or bicycled to school (National Center, 2011). In 1969, 41 percent of children in grades K–8 lived within one mile of school; 89 percent of these children usually walked or bicycled to school (U.S. Department of Transportation [USDOT], 1972). In 2009, 31 percent of children in grades K–8 lived within one mile of school; 35 percent of these children usually walked or bicycled to school (National Center, 2011)."
[Source](http://guide.saferoutesinfo.org/introduction/the_decline_of_...)