The importance of playing the player

I had a crappy session last night on Ultimate Bet. I normally play the $0.50-$1.00 No Limit table with $100 buy-in and I usually scrape a few bucks off of it. Sometimes I'm up and sometimes I'm down but I'm usually up in aggregate. Last night, however, I blew through my buy-in on 2 hands against the same guy. The first hand, about 20 minutes in, I was able to limp in on the big blind with 10 8 offsuit and the flop came 889. There was about $4.50 in the pot so I made a $3.00 bet, which I thought was small enough to induce a call from somebody drawing but large enough to chase out complete trash. The turn came up a seemingly harmless 2. It was now down to me and two others and I bet $7 to see where I was at. The pot was around $13.50. The first player folded and the second player, on a short stack with $35, raised to $20. A range of possibilities went through my head and I narrowed it down to 3 possibilities. He had A9, A8 or a pair of 2's in the hole. I should have folded right there, especially since I was relatively new at the table, but I reraised him all in and he showed...a pair of 2's. Blech.
I lost half my stack on that hand and had to do some battling to make it up. This is where playing the player comes into play. Twenty five minutes after my last beatdown, I got As10s in early position and I raise to $3.00. I get two callers, including my nemesis. The flop comes up with 9s 6c 6h, a nice board. I check, the second player checks and my nemesis bets $5.00. I don't put him on a pair given his play so far and I figure this is an opportunity to semi-bluff. I have two good high cards and I could be leading right now. I also have a backdoor flush draw and two over cards. I move all-in with my remaining $35 into a $15.50 pot. The first player folds and my nemesis thinks for the longest time before calling me. He shows down...AJo (!). He made the right read on me and even though the 6s fell on the turn, I couldn't get one of the many cards that would have helped me (17, if you're counting).
What did I do wrong? Against most players holding AJo in that situation, I did the exact right thing. But against the guy who took me down 20 minutes earlier, I gave him motivation to call me. Look at it from his situation. He cracked my made set with a 2 out draw to the tune of $50. He thinks I'm going to be steaming, specifically at him. So when he sees me come over the top on HIM, he thinks there's a strong possibility I'm bluffing, and he's right. He makes the call and busts me out. And that's why it's important to play the player and understand what HE/SHE might be thinking and not just what your hand is. These motivations can guide the right bet, which in my case should have been a call or fold.