heritable

Height might be 50% heritable in one area but 75% heritable in another, for example (even with the same genetic population in both areas).

If this is based on DNA-methylation, does that mean the 'damage' is heritable?

Various sources of evidence show that IQ is heritable in humans, but depends heavily on the environment.

A lot of heritable diseases are recessive traits - dominant genes are easier to select against.

So every trait can be heritable, but often they only are about half the time?

IQ is strongly heritable (0.5-0.8) and is strongly correlated with lifespan and income.

Since IQ is heritable, kids from more successful homes will be more successful.

It's pretty well supported that intelligence is heritable and greatly determined by genetics.

How much of that was socially determined and how much based on psychological and other heritable traits I don't know.

Cat weight would be heritable, strictly speaking, but in a different environment - all cats get the same food - it would not be.

And so on - why wouldn't these things be adaptable and heritable?

Indeed; also note that traits like intelligence and motivation are highly heritable, so the lottery metaphor is not as outlandish as it might seem.

The central problem is that people don't understand what "heritable" or "genetic" really means.

'The central problem is that people don't understand what "heritable" or "genetic" really means.' Apparently so.

"Intelligence" is by far the most debatable target for this kind of nonsense because a) it is controversial as to whether or not anything like "g" is an objectively real feature of human beings; b) it is extremely controversial how heritable it is; and c) even if it is real and heritable, our ability to measure it is so poor that it is very difficult to make any claims about population statistics.