Seems reasonable to me. I would expect to fold out here a lot of high card combos that beat us. I would go a touch smaller is the only thing, I would just bet half pot. Obviously this is going to make very little difference in the long run given how small the pot is, but it's one of those spots where I feel our sizing does not matter. If he is folding he will fold to any bet and if he is calling he will call any (reasonably sized) bet.

when people limp I like to raise any 2 and cbet most flops and good turns if called. They have a weak range so can't stand a lot of heat. I avoid doing this against total stations though, better suited to weak tight players.

I would bet turn and river once he checks. You should get enough folds from 9x or worse.

I don't mind the check pre with a trash hand because most SB limpers will call anyway and our hand is trash.

This is either bet turn bet river or check-down hand. Betting the river alone is probably not enough to give you enough fold equity and you still have some super marginal showdown value given how passively the hand played out.