It might be a matter of if this person can represent the gospel of Christ and Christians in general. People like to take singular examples from a group and then highlight their real of perceived flaws as representative of the whole group while ignoring the good they do. Happens all the time.
So can being grossly overweight give others the excuse they are searching for to reject the gospel? Possibly. Some people will accept any excuse, even when it's illogical, to reject the gospel.
Sometimes it's the presentation of the message: it was too long, not funny enough, boring, didn't like how it made them feel, was too complicated, couldn't relate to the preacher.
Sometimes it can be hypocrisy that turns people away. Sometimes legalism. Sometimes maybe it's their weight.
Other times they can't find a clear reason to answer the gospel call, their answer is simply "not today" or sometimes "not ever."
Some people have their mind made up, but some people are fence sitters and literally just waiting for someone to come to them and drop the good news of Jesus Christ into their lap.
Can't win them all, can't please them all.
I've seen the gospel rejected quite a bit and I know how bitter non-Christians talk about Christians when they think no one is really paying attention.
Biggest reason the gospel is rejected, in my experience, according to what I've heard, not enough love and kindness. People rarely, if ever, say "they were too overweight to preach."