When I first started riding more seriously, I was riding a single-speed and intentionally avoided hilly routes. But after a while, I figured out that if I was going to get better, I needed to seek out the hills rather than avoiding them, and that seems to have been a good strategy. I've been riding a geared bike the last 18 months or so, but I find that the average Texas hill isn't a problem. Wind is, and heat is, and too many hills too big are, but otherwise hills are just fine.
One thing I did with the single-speed was that I tried to never walk a hill, and think I just did that twice on small rises that were too steep. But whenever necessary, I would stop on the way up and rest a moment. Pacing also becomes an issue, and if you find yourself already exhausted at the bottom of the hill, you're not going to do yourself proud going up it, either. I ride with some groups that are basically just faster than I am, and there are times when I can hang with them and times when I need to do the ride at my speed.
I've been ever-so-slowly losing weight and that helps. Having a good light so I can ride year-round helps (I've got over 800 miles in January). Riding into the wind (either solo or pulling) sucks, but does make you stronger.
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"be careful this rando stuff is addictive and dan's the 'pusher'."