Ahead of his range but unprofitable to push?

[JFsports]

interesting post, my default would be to always push here. Villain's can have draws a lot of the time, or if they don't they can 'put you on a draw' and call with one pair. Imo, (to not shove here) you need an iron-clad read that
a) his raising range does not include any draws
b) he will fold all the one pair hands you mentioned to a shove.

If these are both true, then I would call and either c/c turn or bet it myself, depending on what your read is. There are no real scare cards that can come from your point of view as you say he can't have draws.

[kolotoure]

this is live i.e. an easy shove

[ddrstel]

If this is a live £1-£2 game in London, i shove and fist pump when he calls.

The action hardly dictates to that of having you beat right now.
I personally would weight a range here more towards AA/KK/AQ, with sets making up a tiny part of his range. The reason is people love to slowplay live, and with so many people left to act on the flop i imagine he's calling sets far far more than he's ever raising them.
There's also the small chance he makes a hero call with KQ, "putting you on a draw because you played it so fast".

Given these assumptions i believe your equity here is much better than you originally assumed. I think you should include AQ and KK within his calling range.

I also don't mind calling and donking 60-80 on the turn, but there are a lot of cards we don't want to see.