I think this is quite a elementary fold or shove situation. Would calling even be an option?

Effective stack 315. 5am 8 handed.

Hero (UTG) raises 8 with AJss
4 player calls, including Villain who is relatively capable and aggresive (SB)

Flop (40)

It comes J73, two-tone with two diamonds.

Hero leads 35, folds to Villain who raises to 125.

Hero??

My immediate thought process was that the flop is moderately wet, which gives Villain a good opportunity to semi-bluff, especially given that he's last to act. QQ+ is pretty much out of the question. 2p+ is unlikely to be in his range either. That leaves sets to be the only hand that currently beats us. However, my range is clearly capped which Villain should be aware of.

Are my thoughts flawed by any means?

Your range is clearly not capped.... Villans range is more likely capped than yours, best possible hand at the moment is JJ....I really hope this is in your open range....is JJ in villans calling range. Maybe not, but 77 will be, so whatever, he is capped at 2nd nuts....

Flop is a pretty clear call Imo.... We need to leave villans bluffs in, by raising villan can only continue with either stuff that is already beating us, or draws with big equity against us.... By calling here we allow villan to continue with a bluff as our hand is quickly becoming a bluff catcher.....
Hero calls,
Checks all none a/j turns, and maybe even those we check.... Then we can fold if draws get there, the 8d would be a good candidate to fold, but most cards we check call, and then, look at what happens at the river.....
Being oop sucks

Apologies as I think I used the term wrong - Yes indeed I can have JJ maybe even 77 on some tables.

I wonder, however, wouldn't calling and checking OTT give Villain a very good price to see the river which is something that we wouldn't want to allow from happening?

Well we are stumbling around the elephant in the room that is position..... It's not ideal but oop we just don't really have a better option, raising/jamming the flop will just serve to get called by hands that have us crushed, or hands that have 40+% equity against, we're as it only really folds out worse hands and villans bluffs....
We have to call, and it allows villan to continue with a bluff, which allows us to extract more value, but we have to be good enough to fold if it looks like villan has binked....
Again turn is a check for much of the same reasons, we are only getting any value from villans bluffs / semi-bluffs so we have to give him chance to bluff.... Leading just allows him to fold when he is behind and call with good equity or when we are crushed...
I am assuming we are oop to villan because of flush action, although you say villan is sb pre-flop..... This hand in position is very different...

Villain is SB, no?

I think I now fully understand the reasoning behind your suggestions and thank you. Would be great if you could comment on my decision, commented below.

Indeed. He check-raised and sorry for not making it clear.

Decision:

You should have overpairs, sets, plus strong combo draws (AdKd, Td9d, etc) in your range here. I think folding here is fine.

Thanks for your comments and perhaps I am a bit MUBSY but I certainly agree with your thoughts. AJs is nowhere near top end of my range and has limited ability to improve. Perhaps I can take the call-check line with better holdings.