It doesnt matter since you need a really good read to assign such a narrow range. Villain will stack off with random junk like QJ/AJ/KJ and also JT so that getting it in is profitable. I'm not saying he's always stacking off with these hands but saying he never is is also wrong.

Yes, there will always be those who stack off with bottom 2 pair on a monotone board

Both boards are super wet. Especially given the possible turn & rivercards, I'm investing the absolute minimum in both hands, until I improve.
You can argue that you might very well be ahead, which is true, but if your opponent is happily shoveling money in the pot, alarmbells should be ringing (even at 2NL)

Hand 1- When he 3bets, alarm bells should be going off that he has the straight (and possibly a higher set, though much less likely). It's also possible (though rare) that he would be doing this with AJ or two pair. For math purposes, I'm going to assume he always has the straight here:
Something to consider is that there is ~$3.25 in the pot and you only have $1.30 left. So, it's going to cost you $1.30 to win ~$3.50. That's 2.7:1.
You need to make a fullhouse or better to win, and you have ~28% chance of doing that by the river. You're getting a price good enough to make a small profit.

Other considerations:
1) Sometimes villain is going to have a better set than you.
2) Sometimes villain is going to be doing this with AJ, 2pair, pair plus straight draw.
In my experience, #2 is much more likely than #1. This makes it a clear shove in my book.


Hand 2- Entirely villain dependent. I would slow down when I got raised on the flop and possibly fold the turn to a decent sized bet. Villain doesn't have much left behind, so you're not getting great odds to draw if you are beat.