t4e is one of the best people to speak to regarding heads up play, but I'll take a shot and tell you how I play HU matches.
Basically from hand #1, I'm raising every face card, and am basically trying to dominate my opponent. If he's passive enough, he won't call my raises with anything but a class 2 hand or better - by this I mean KQ AJ and
88 type hands and better. Basically I never limp, and raise about 75% of the hands I have, or even up to %100 if OP is passive enough. I also raise the exact same amount every time.
Another reason I do this (aside from the obvious blind stealing and taking control of the match), is so that I can conceil my premium hands. Say I've been folding %75 of my hands instead, and out of nowhere come in with a big raise, my opponent will read me like a book and know I have a top 10 hand.
Most of the time you will both miss the flop, so instead of checking down i like to be the aggresor and take down those pots.
I hardly used to play HU, but have been playing it alot more recently, and one of the harder things for me was getting used to the frequency of different hands post-flop. ie how often you see top pair, or a set, or a straight etc etc.
For example, top pair is nearly always ahead, and I almost always bet middle and bottom pair, but being cautious if I get called or raised.
One thing to keep in mind though, is that I've lost and won so many matches because of kicker troubles - both players might hit top pair and go to war, and this is something to be very careful of. If you get raised when you're holding top pair, medium kicker, be cautious.
But basically unless I get a big reraise, or a strange cold-call (possible slowplay, or draw) then I'm betting like I have the nuts.
It sounds like you're getting bad beat, which is nothing to worry about - those will even out in the end just like any other type of poker. Don't start thinking that since you have been beat with 2 pair vs. someone's set that you should play 2 pair more cautiously - 2 pair and up are monsters headsup.