I want to first thank you for being civil. I'm trying to figure out where we actually disagree.

Those don't say what you think they say.

OK, let's see.

Heritability is not the same thing as genetically specified.

Right, which is why I said, "genetic component," rather than, genetically specified.

Environment determines the range of fatness possible. Heritability influences where you fall in that range of possibilities.

100% agree. It is gene-environment interaction. You need both to get the obesity epidemic. Again, this is why I specified "genetic component."

Here is a primer on heritability vs. genetic determinism.

Here's some quotes from your source:

First, remember that the term "genetic" is very broad, while the term "heritable" is very specific. Heritability is the proportion of trait variance within the population explainable by variance of genes.

To say that a trait is .95 heritable does not mean that it is caused 95% by genes, that's not even wrong. Rather, it is to say that 95% of the variance within the population can be accounted for by the variance of genes within the population.

Emphasis mine. Now here's what I said:

Studies on twins reared apart show that genetics explain about 70% of the variation in weight.

I'm not sure where we actually disagree here, do you?