A 40% openingrange looks like this:
{22+, A2s+, K2s+, Q4s+, J6s+, T7s+, 96s+, 86s+, 75s+, 65s, 54s, 43s, A3o+, K9o+, Q9o+, J9o+, T9o}.
On this board I wouldn't look at the cbet stat, imo there's some chance he's cbetting close to 100% of hands because the board is generally good to cbet.
So the first question is: do we want to call the cbet to move him off of his hands later on, or try to take down the pot right away.
When you're >200BB deep I think it's better to raise right away.
The reason is, that you want to put pressure on the opponent - not only to get better hands to fold in a spot like this, but also to maximize value when you have a monster.
By calling 2ndpair with a FD here, you limit yourself to calling stronger hands as well - or you polarize your raisingrange, but this isn't the best idea either because you don't hit a strong hand too often, hence you can't bluff too much as bluffing a lot would immediately result in an unbalanced range (and in this spot it is kind of obvious).
Besides all the balancing and metagame stuff you can also argue that your hand is pretty weak wo you'll hav a hard time on basically any turn, therefore we put immediate pressure on the opponent and if he happens to call with even Kx we usually have >40% equity due to >FD+2pair outs.
As played on the turn I think it's definitely possible to raise in general.
However, given you have an aggro dynamic going, a fold is probably the safer play.
If you raise and he calls I think you should bet the river as well. I thought about overbetting, but it's a matter of how he thinks. If he's the type who likes to herocall I'd rather bet slightly more than 1/2 pot to make it look like a valuebet.
Otherwise an overbet is fine, too. We can rep nutflushes for the most part.