I would have played this the exact same way. We beat so many hands, 66/77/99/TT and overcards with clubs along with funky hands like T8s etc.
If we have any notes on the villian that he calls 3bs with hands like QQ then we should definitely be weary after getting called on the flop.
We should also look at his 4b stats and if he never 4bs then thats massive alarm bells if its a decent sample size.

We can even consider our own image, and if we're getting out of line and 3betting lots then we have to consider our opponents may get smart and try to trap us with these hands.

1 hand isn't enough to draw a conclusion, but this definitely isn't bad play. Take notes on the guy for future

JJ seems close here. A way to try to figure out if you should value bet or not is by thinking about what villain will call with. Obviously harder to do while playing but now that you're off the tables you can take a look.

What type of hands goes he get to river with? Just big pairs like TT+? Will he often have stuff like AA/KK or might he 4bet those pre. What about low pairs and sets? Stuff like 98s? A8s? 67s? A-high floats? Flush draws?

Write out what hands you think he gets to the river with and calls the shove. Among those hands how many are you ahead of and how many beat you? Then you can get an estimate of tight or how wide you should be value betting. Post them here and I'll definitely give you my thoughts and I'm sure others will as well.

We have not so much hand with him but when he raise from MP and we 3bet him he will think we have strong hand. And if he continue he will choose strong hands too.

22+, A2s+, KJs+, QJs, JTs, T9s, 98s, 87s, 76s, AQo+ can be nice range for him.

On flop he can continue with all of them.

Turn QQ+,TT-99,77-66,JdJs,8d8h,8d8s,8h8s,5d5h,5d5s,5h5s,4d4h,4d4s,4h4s,98s,AcKc,AcQc,KcQc,AcTc,Ac9c,Tc9c,Ac8c,Ac7c,8c7c,Ac6c,7c6c,Ac3c,Ac2c (%5,92)

River he can call us QQ+, TT-99, 77-66, JdJs, 8d8s, 5h5s, 4d4h, 4d4s, 4h4s, Ac8c, 9d8d, 9s8s, 9c8c, 8c7c, 7c6c, Ac3c (%5,09)

We can beat TT-99, 77-66, Ac8c, 9d8d, 9s8s, 9c8c, 8c7c (%2.68)

But i thing good players never shove us Ac8c, 9d8d, 9s8s, 9c8c, 8c7c.

So if i bet that board bet for beat TT-99, 77-66. But if i check most of the time he will check too.

With all of that information check/fold better option for me.

Don't 3bet pre?

I agree with Milfgrinder. No need to 3 bet this pre against a reg. Calling is fine in these positions.

As played I like bigger on the flop, turn is fine.

Once we see the river though I doubt we can bet for value against a solid opponent. Again because of the positions I would expect a thinking player to be able to get away from TT or worse. If he has QQ JJ it's doubtful he would try and value bet himself because many micro stakes players with KK+ in your position would check the river on this board once it pairs because they're so passive.