Raise J9o on the button instead of limping; the postflop line is fine, but we lose most EV preflop.
Flop K♠8♦9♠ in a limped pot on the button, we have middle pair plus straight potential vs a very wide BB range. This is a great texture to bet small for value and protection versus overcards and random gutters. Checking back is okay and keeps the pot manageable, but we leave some straightforward value on the table.
Turn pairs the K: K♠8♦9♠K♥ after BB checks again. In a limped pot, BB doesn’t have that many strong Kx, and our 9x will often be ahead of 8x, underpairs and random floats. Betting 1.5 into 2.5 is a reasonable thin value/protection stab that also picks up folds from his air, as we saw.