I'm a new losing poker player, I keep finding my self in difficult situations like this. I put the BTN on 22+, A9s+, K9s+, A5o+, K9o+. Anyway I can play this better, or fairly standard situation?

No Limit Hold'em Tournament T60/T120
Buy-in: $0.49+$0.06 USD Hold'em No Limit
PokerStars
9 players
Formatted by pokercopilot.com: Poker HUD for Mac and Windows

Stacks:
UTG - UTG (T9,160)
UTG+1 - UTG+1 (T13,825)
UTG+2 - UTG+2 (T3,700)
MP - Hero (T4,712)
MP2 - MP2 (T4,988)
CO - CO (T10,072)
BTN - BTN (T22,923)
SB - SB (T5,079)
BB - BB (T4,590)

Preflop: (T288, 9 players) Hero is MP with 4 4
3 folds, Hero raises to T240, 2 folds, BTN calls T240, 2 folds

Flop: 3 A 2 (T768, 2 players)
Hero bets T384, BTN calls T384

Turn: J (T1,536, 2 players)
Hero bets T787, BTN calls T787

River: 6 (T3,110, 2 players)
Hero checks, BTN bets T21,500 (all-in), 1 fold, Uncalled bet of T21,500 returned to BTN

Total Pot: T3,110

BTN wins T3,110

Why would he have A5o+ but only A9s+?

There isn't really any reason why you need to bet two streets with 44 when you basically have 3 cards in the deck that are good for you. Bet once and give up or x/c the flop I prefer betting once and giving up, maybe on the turn depending on teh card as your range is very Ax heavy I assume and the board is pretty dry so you don't always want to be betting all your Ax.

I usually give up with underpairs after one stab on Axx flops like this. If you're lucky, villain will check back the turn quite often, whether he has Ax, 99/88 or some kind of draw. 44 isn't a great hand to triple with, and it's probably a bad idea to barrel if you're going to give up on the river, so this is one of the combos I'd be one-and-done with. Sometimes I just check-fold the flop, or even fold pre, as small pairs play so badly OOP.

I mean, if you go back to the flop, it probably makes more sense to c-bet with KQ/KJ/KT/QJ/JTs in diamonds or spades (or any KdXx hand with the BDNFD), as they can all turn something you can barrel. With 44 (especially in those suits), there's so few turn cards that are good for you.