But the modern United States diet is not "a lot more Paleo".

You're wrong. 1961 USA was already quite far in its transition away from Neolithic food, it just takes time for such low-level damage to accumulate.

There's little high quality world-wide data before 1961, but feel free to offer a bet about it if you doubt what it would reach.

Correlation goes the wrong way, just like I said.

In any case, obesity statistics are easily available for all countries, so I'm puzzled by your unwillingness to take a look.

Moreover, my impression - confirmed when googling this - is that the warning against sweeteners and vegetable oils is an important part of the paleo critique of the modern diet. If you follow paleo advice, you will abandon sweeteners and vegetable oils.

It's not. Paleos bundle all non-Paleo foods as if they were pretty much the same. It's about as useful as abstinence-only approach to safe sex.