Exponential growth doesn't grow forever, when talking about populations the curve is more of an "S" shape due to upper limits. After a point it turns into exponential backoff as herd immunity is approached.
And you're right that overweight/obese doesn't follow either curve, but what you're missing is that it's already really high, and pretty stable at that point.
It's kinda like arguing C * O(n) is worse than C * O(1), but completely ignoring that in practice n < 10 in either case, but C = 1 for the first and C = 100 in the second.