Yes & no.
I'm not embarrassed to like the type of guys I'm attracted to, and while I care less and less what anyone else thinks I do still have a bit of apprehension/anxiety about being completely comfortably out to everyone as gay. So yeah, there's the gay thing. Fortunately I don't look or act "gay," so it's not obvious to people.. and I'm still going through legal proceedings re: homophobia. (see lgbt forum) However, the whole legal thing hasn't made me more closeted, it's made me waaaaaay more comfortably out as I've had to come out to a bunch of old coworkers throughout this process and it's accelerated my learning that pretty much no one else cares these days save for the odd homophobe out.
I did hear a few homophobic comments this morning (not directed at me nor as a slur) and I just laughed. The guy figured I was laughing because he was being funny or I was agreeing with him, but really I was laughing at his perspective on things and wondering why he'd give a sh** about some gay radio dj talking about his boyfriend any more or less than a hetero dj talking about their partner. He was concerned about having to explain to his son one day wtf is going on if he heard that on the radio.. I kinda thought his son might not wonder so much about the relationship he heard about on the radio so much as why his dad seems to think he should have a negative opinion about it. Hopefully his son grows up with a more evolved crowd.
Back to the topic at hand.. the type of guys I like aren't an aesthetic group that are commonly found to be unattractive by some groups as is your situation with liking bigger girls. Not trying to be a jerk here in the least bit, just straight (gay? :p) forward about it. So, I don't have that mental battle to overcome in terms of anxieties about others judging something like that.
In the end, we all have our types, and who gives a flying f**k what anyone else thinks of what we as individuals like? What we happen to be attracted to isn't up for debate with anyone as to whether or not our type is attractive, as obviously they are attractive to us. Just stop caring what other people think and you can't be embarrassed in the least bit by it.
. Whenever I've tried to come out to people they usually don't believe me. Luckily for me I don't really have a strong preference for bigger girls, I just find a lot of them to be attractive. At least when they're feminine. I also have a stronger preference for blondes which is pretty normal and acceptable. My strongest preference is actually "edginess". I'm glad that I have that preference because most "edgy" girls aren't straight. Even if they look feminine.