I’m embarrassed of her?

I met this girl on bumble, she looked chunky but when I met her today she looked even chunkier, she didn’t catfish me, I think she just got creative with her angles, I wasn’t blown away and she’s not like 300lbs, my brother and his friends gave me a “oh my god” look when she turned away. She’s a great girl and has a really pretty face, I personally don’t really care about her weight, im not really looking for perfection, but I noticed when I was being seen with her that I was pretty embarrassed, and at one point kinda hoped that people would think she’s my sister or something. And after thinking more into it I would be pretty ashamed to show her to my family, I can tell she’s an amazing girl, she’s definitely deserving of a guy who doesn’t have the feelings I do, I want to break it off, but I don’t want her to feel any sadness at all, I really had no idea she was as big as she is. and even though I don’t care about her size, the fact that I feel shame, I feel as if she deserves better than me truly. Any tips on how to Sabatoge this to where she doesn’t have to feel bad?
I’m embarrassed of her?
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