A check on the flop opens your opponent's range up a bit and is defs the preferred line against anyone decent. Once you bet tho, go with it imo. You're not that happy about it, but as already posted, you have some equity when called and if villain is ever folding a shove is just so full of win.
What's your checking range here assuming i'm 3betting this spot on the tighter side? I think i'd continue with almost all my value range, KK/QQ hands and also any bluffs, so i'm not sure if i should have a checking range at all?
Pretty sure i never c/b this board unless i have air/draws.
Betting nearly always gets through so with our value hands its pretty meh