Disclaimer: my perspective is almost certainly not the norm, or objectively true.
I don't care if a girl is "thinner" if by that you mean "lean". If you have more fat than muscle overall? I really don't care.
If you are obese, or morbidly so, yes it will be an issue.
Let me clarify that deep down I do not care if you are obese. The source of my aversion is driven by evolution.
I hate sanitation, organization, sleep, finance. It all makes me miserable. But so does the prospect of eternal solitude. Life is a balancing act. Do I wish I could marry some rich pornstar/queen? Sure I do. But it won't happen, and developing such an expectation is downright psychotic. And do I even deserve such a life? What would someone have to do to earn such a fate?