I guess I'm echoing what other people are saying but: yes, you raise that river, no you don't shove it. Although chances are he puts all his chips in any way.
PF: He limped his 9s. This leaves his holding pretty disguised. This is either a) clever if he knows he has someone aggressive acting behind him, or (b) really stupid because it's a waste of a strong holding.
But at this point it's easier to put him on speculative hands or top premiums honestly (AA/KK/AK/AQ).
Flop:
Kc9s7c
Villain leads out 25, into what I'm supposing is around 30 in the pot. So almost pot sized. I actually like this donk bet because there's a fair amount of kings in your range, and it further disguises his hand.
What it looks like to the outside - he has a king and he's protecting it from a fairly draw heavy board. What it looks like to you IF you were to have a king (from his perspective) - he is repping a king, or possibly AA but in reality has a draw. JT, T8s, Ac4c.
Turn:
3d, the brickiest brick of all the bricks.
He checks which kind of reinforces the draw concept. You bet 45 - I don't love this bet. You're betting 45 into 80, so your villains essentially getting 3:1 on a call. In a 200NL this isn't max value you can get from a draw and doesn't really tell you much about where you're at. 60 I think would be better. Anyway, right now the easiest hands to put him on are draws.
River: 7d
He leads out again and bets 15 into 170. Given his holding I hate this bet. But I understand what he's trying to do. He's hoping YOU have a flush here, or at the very least AK and is putting in so little that it's essentially just a check. Except it's a check that requires you to now value bet a little higher than what you would have value bet otherwise.
However, unless he's a super-reader jedi master, this bet takes all the draws out of his range. This puts him on a most likely range of: A7 (4), K9 (6), QQ (6), AK (12), KQ (12). But how many of those lead out the flop and then check the turn? A slow played K9 and QQ are the only hands in that group that makes sense. so 10 combos of legit hands, 40 combos if you include missteps and weird plays.
The only other option here is that he has a monster and either wants you to
bluff the diamond flush or legit raise for value with your A7/AK/whatever value hands you might have. What monsters are out there?
99 (4), 33 (4), Ace Rag diamond (5), maybe JT/T8 diamond sometimes (I'll credit 1 combo). So, like 15 legit monsters, of which you are beating 11.
So of 25 legit hands you're beating 21. If you count bad plays you're ahead over 90% of the time.
But what calls you when you shove? Only monsters. Half the sensible hands, 1/3 of the overall combos. It's not the worst shove in the world, but I think you can get more value by betting something like $90. And we're really playing for value on this river.