My (27M) wife (27F) does not like me showing off my body at all and gets incredibly insecure over it. She recently broke down and told me that she is petrified I will 'run away' with a more beautiful woman.

We got married 2 years ago and dated 3 years before that. I do not have some super buff body or anything, but I do go to the gym relatively often and watch what I eat. My wife has always been a bit chubby, but she is still very beautiful. And that isn't just my view, she was known in our friend group before we dated as a very beautiful woman.
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Regardless, she has an incredible amount of insecurity over my body. She wants me to cover up in public basically. She constantly presumes people are looking at me sexually. She sort of chastised me about wearing a sleeveless shirt to go play basketball, saying that other women will be looking at my arms. She took me to the side at brunch and told me to button my shirt up because my chest hair was showing. I lifted my shirt to wipe sweat off my face during a picnic and later she was like "did you have to show off your abs like that? people were probably looking". She has a weird fixation over whether my pants/shorts 'show my bulge' or not (they do not, but she seems to worry they do). She literally requested to her sister for a pic of us at her pool to be taken down because I was shirtless in it. That was kind of the straw that broke the camels back. I have talked to her about this, but usually just give in. This time I genuinely confronted her about it.
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At first she was just saying that it was a jealousy thing. And I think it is, to an extent. We had a discussion about it and she agreed that she would stop being so controlling. But then she broke down and said that she 'cant stand' the idea of other women looking at me, saying that she constantly is terrified I will leave her, that her worst nightmare is some beautiful supermodel girl coming up to me at the gym and flirting while she isn't there. She said that she can't imagine still picking her after a beautiful woman flirts with me. She also commented on the fact that I had only had sex with one woman before her, and that she doesn't get why I have no interest in ****ing the 'countless' women who would want to **** me. She cant comprehend it. She said that she has tried keeping this from me but she can't anymore. And so she went back on what she said before, and asked that I just please respect her wishes for me to be modest just for her sake. I said okay, I will, but I think I only said that because she was hysterically crying. Needless to say throughout this conversation I told her many times that what she said was not true, that she was beautiful, that I would never leave her etc. All of that is true, I wasn't just saying it to comfort her. I told her specifically that she is pretty widely known in our social circle as a very beautiful woman, its not just me telling her that. It was in one ear out the other.
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I was just flabbergasted. For one, I had no clue she viewed me this way, as some type of guy who could apparently sleep with supermodels any time I please and apparently is constantly approached by them (again, not true). I also had no idea she has this incredible fear that I am going to leave her if this happens... I would never do that. I thought she knew that.
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I just don't even know what to say now. I can only reassure her so many times. It feels like nothing I say breaks through to her in terms of me telling her I would never leave her.
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What do I do? Its the morning after. She comes home in two hours.
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TL;DR - - wife broke down and told me the reason why she always asks me to cover up is that she hates the idea of other women lusting after me and she is petrified i will leave her for a more beautiful woman


Source.