Unfortunately, many men (and women) on dating sites don't even bother reading the profile and only look at the pictures. The just send a thoughtless "hey" message to many people hoping to get a response. I found this most prevalent on free sites.
I personally met my fiance on eharmony (pay site). I liked that the site matches you based on your interests/beliefs and what you are willing to accept in a partner. One section of the questionnaire had you select how you would define your weight category and also what weight categories you would date. That way I wasn't matched with anyone who wouldn't date overweight women (as long as I answered truthfully myself).
Just letting you know that the right person for you will contact you at any size