An interesting dynamic in this hand is that the board has a lot of draws on it. This makes raising the flop and checking behind on the turn a less attractive possibility, and was something I just started thinking about more closely when I rode my bike to work (it's what I think about when I ride my bike, what can I say).
I now think raising is a mistake against all but the most straightforward of players that we can trust to always represent exactly their strength, i.e. who would call our raise with all hands that we beat and only raise us when we're (well) behind.
His range when he bets the flop is,
1) Pair-type-hands. QJ, AJ, AT, J8, etc.
4) Complete bluffs like K7 that just want to take a stab.
Against pairs, we want to raise. Against 2p/sets, we want to either get away cheaply or see a cheap showdown. Versus draws, we want to get more money in now, but against bluffs, we want him to keep betting.
The difference between the trustworthy and tricky players is not what their range is after they bet, it's how they react when we raise. A trustworthy player might bluff at the pot, but not re-raise bluff. He will reraise with his strong hands, but just call with his weaker holdings. And he will fold his bluffs when we raise.
But since we raise with the intention of folding if our opponent comes over the top, it seems to me we have to focus our raises on players whose "over-the-top" raises we can trust.