Further to above...
Climbing is really the only way to strengthen yourself for climbing, so if you plan to ride more events like the one last weekend, it might be worth driving a bit twice a month to do a long ride with some serious climbing. Also, yeah, you need lower gears. Getting a 12-25 or 12-28 cassette would do wonders - I assume you're running a triple?
About losing weight - yeah, that'd be great, but it's also possible for us heavier riders to become better climbers. You just have to do it. And the more you do it, the better you'll become. You can find lots of videos with advice on climbing, but the key is finding your own pace. As a heavier rider, you'll probably want to stay seated, but also, for the steep pitches like inside switchbacks, standing up can help you power through them. Standing up is another thing that benefits from practice. If there are any 30 second steep pitches in any of your nearby moderate hills, start doing them standing, probably going 2-3 gears higher than you'd do them seated. 3 years ago, doing 10 seconds of climbing out of the saddle was really difficult, but I started practicing doing it for longer and longer stretches, counting the pedal strokes, and now I can do it for a lot longer.
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