You can contibet the flop a bit smaller. The board is very dry. Rangebetting with 1/3 is good in the low limits. This is the standard in the beginner strategy.
Opponent calls so probably has something. I don't think cold callers have a lot of 5s or 3s, so a Q is most likely. Checking behind on the turn is good play.
On the river your 9 is paired so you have trips top kicker. Very unexpectedly the opponent open stacks off for 7x potsize.
Ok, this is something that needs a little time to think about. You are at the very top of your range. This is the absolute best hand you can have. Therefore you can't fold if there is a minute chance that the opponent could bluff.
This I can't judge because I have no reads of the opponent. I have no indication that he is unreasonable and would do such extreme moves with a bluff. However, I have seen a lot of strange things players do when the board pairs.
Are there weaker hands that the opponent would like to bet for value this big? It's most unusual to do this with top pair because this move creates so much foldequity. However, if your opponent is convinced that your hand is worse than top pair because you checked behind on the turn it may be possible. I don't see him calling with a 9 on the flop if he isn't a hard calling station. Every 9 with a backdoor flush draw on the flop is covered by the board or by you. The last 9 didn't have a backdoor flush draw on the flop.
So it's: a bluff, a full house that was slow played on the flop or is Q9, a Q where the opponent couldn't help but push it.
You need to be good 45% of the time to call because the bet is so big. No flush nor straight is possible.
I think I would call. This is so extreme even with a full house that I think there is not a small likelihood that this is some spew.
Even a full house has to consider which hands would call. Against such a large bet you could fold almost anything. It is highly unlikely that you hit the freak 9. Your range is indeed pretty weak. It would be much more reasonable to bet the full house with a size that could be called with a bluffcatcher. If you had the 9 you would raise a small to middle sized bet anyway. So there is not a lot of incentive to just push the full house.
Opponent's move lacks logic. Against unlogic I like to see what's going on if I have serious showdown value.