Hi, I was with my STBXH for 16 years so I know what you mean. Also I am 39 and overweight.
I joined a dating site to do some research into what single men of my age are out there and to get some feedback on my attractiveness as I have been out of the dating scene for so long. I had intention of starting a relationship.
I was totally overwhelmed with responses/messages. I literally couldn't keep up/respond to them all. I think that there are a lot more men than women on them in general.
I read somewhere about having a "dating phone" to allow contact but keep some privacy/distance. I bought a cheap mobile and a PAYG sim card. It was great advice.
I went on about 10 dates, kept it very casual, just enjoyed meeting and chatting to new people etc. All the men I met seemed really nice people actually, not at all like the horror stories I've heard but maybe I was lucky.
I had a quick fling very early on to get my STBXH out of my system and to get having sex with someone else out of the way.
I always told someone when I went on a date, sometimes it was just texting a friend etc.
I was about to cancel my membership when I met my BF, been together 4 months now. Very happy. I had a good feeling about him early on and actually gave him my real contact details straight away, may have been a bit silly.
I think some general advice is to meet any potential dates quite quickly so you have chance to see what they are really like and you don't build up unrealistic images/fantasies in your head, only to be disappointed when you finally meet.
One thing, if this man is talking about you being sexy, he may be after sex predominantly. Which is flattering and great if you are too. But just bear it in mind. My BF never said anything remotely sexual/flirtatious before we got together and he is a real gentleman, very considerate, mature etc.
Oh and apparently, sites that you have to pay for are supposed to attract less wierdos than free ones.
Good luck