Like what others have said, you need to bet higher amounts and be more aggressive. I apologise in advance if my analysis offends you, but I'm going to be very direct with everything you did wrong so that you can improve for the future:
Preflop: you should have re-raised to somewhere between $0.18 and $0.20. You don't want to price people in to set mine or play marginal hands like suited connectors.
Flop: You should be betting a lot more. You bet 40% of the pot, but on a draw heavy board you need to bet aggressively. You can easily bet $0.20 here and expect a hand like Qx or Tx to pay you off. Think value and bet higher amounts.
Turn: I would avoid the check-raise here and just continue betting yourself. You don't want someone with a flush draw to get a free card, just as you don't want someone with Kx to hit a Q on the river. I would value bet about 70% of the size of the pot. If you are going to check-raise, you should raise higher to at least $0.60, possibly even $0.80. Think about it this way: if the villain has 2 diamonds, then the villain needs 4 to 1 odds
to profitably call a flush draw. By making a $0.30 raise, the villain only needs to win $1.50 to make it a worthwhile call (and there's already $1.45 in the pot on the turn, plus extra value can be obtained on the river). You want to protect yourself from these kind of draws, which is why it's important to make larger bets so that you don't give the villain the correct odds to chase their potential draws.
River: With only $0.61 left and $1.45 already in the pot, it's clear that you're already pot committed. Don't expect the villain to bluff here. You're lucky that the villain made the bet he did because most good players will just check behind with KJ here. You should take the initiative. You should be the one betting $0.61 and let the villain call you. Don't play so weak. You should be in a value betting mindset, rather than check-calling like a scared, passive player.
I congratulate you on your win, but you need to play more aggressively and think value, rather than being so passive.