u/Few-Canary-8641

Playing Red Rock Casino Resort & Spa 1/3. I’m in the BB with King-Jack offsuit, $415 effective.
UTG (loose player) opens to $10. MP (tight player who hadn’t 3-bet in hours) makes it $25. CO calls, Button calls, I call in BB, UTG calls. Pot ~$125.
Flop: King Jack Four rainbow flop
I lead $40 first to act. Thought process: dry board, I flopped top two, expected weaker hands to call and stronger hands to raise. Also set up a turn jam if multiple callers.
UTG folds. MP raises to $125. CO folds. Button tank-calls. I jam for $415 total for value. My thinking was I block Kx/Jx combos and MP can stack off with Pocket Aces or Ace-King.
MP calls (covers me slightly), Button calls (deep stack; later said if I had ~$100 more he may have folded).
Turn/river brick out. MP gets last ~$50 in on turn, Button calls.
Showdown:
I have King-Jack offsuit
MP has Pocket Aces
Button has Pocket Fours for bottom set
Questions:
Is King-Jack offsuit too wide to defend preflop in BB vs tight MP 3-bet + multiple callers?
Is calling better than 4-betting preflop?
On flop, is lead/jam best, or should I check-raise / just call raise because Button cold-called?
Standard cooler or did I overplay top two multiway?