You're cycling past ppl in lycra shorts, if you're going fast enough they'll probably not notice what you look like. Even if they do you've probably passed them by before they've thought up their witless comment.
You wear them because you're a cyclist and they're the most comfortable item to wear when going for a proper ride. It's practical and common sense to wear lycra shorts. If you cared more about looks more than health, fitness and doing possibly one of the most enjoyable type of exercise there is then you'd probably not cycle. You'd be in a weightwatchers trying to get even more excess weight off by counting food points (but really having a sneaky cream cake on the side to cheer you up because you've not reached your goals...again!).
Sorry for the harsh alternative scenario to cycling in lycra. It's just that if more people did what they wanted and to hell with everyone else thought about their looks I suspect we'd be a happy nation. Although probably a fatter nation because there's more lazy slobs not doing any exercise than there are those doing exercise. Easier to waste money on weight loss tablet and unused gym membership than actually taking good care of yourself.
To the op, it's just my opinion but an overweight person in lycra, on a bike, making the effort to get / stay healthy looks better than someone fat who's doing nothing to get healthy.
Lycra is just a fabric component that aids comfort. You can choose it or choose a baggy mtb/touring but cycle specific pair of shorts. It's about what works best for you when you're cycling. You choose the right components, bike, tyres, etc for your riding. Lycra is just another right thing to choose.
BTW I don't care about my "look". I wear what I choose to wear. I'm mid forties and life has more important things for me too worry about than clothing. So I don't understand vanity and complexes people have over clothing. Besides people who want to judge you on looks will do so no matter what you look like or what you're wearing. Nothing will change that.
