Eeek. This is all frighteningly reminiscent of when I met my now-DH but soon to be my ex-DH online! (Except I kept my knickers on a lot longer than you have. )
I'll give you the advice that I wish i'd been given at the time -- although, TBH, i was given this advice but ignored it (as no doubt you will too!):
DATE OTHERS
Listen to yourself, you are terrified of losing him already and you have been on 2 dates. This isn't healthy keeness, it's terror of losing him. You joke "maybe I'll shag him every night so he can't go and meet gorgeous women", and know you don't mean it, but listen to your panic! You are not thinking about what he can do/add/improve in your life, but in how you just must keep him/hang on to him/trap him.
NO NO NO. Carry on seeing him and this dynamic will 8never go away. he will never* be able to look keen enough to dispel your fears, they will always be there. You could easily become jealous and clingey. I never thought my DH liked me that much, and he married me! It still wasn't enough.
For some reason, we meet one of these types every so often and they make us obsessed. It's really not good. Please, please give yourself a resounding virtual slap, FORCE yourself to keep dating other men to keep this one in perspective, and take steps to boost your own self-confidence so you end up thinking that he should be terrified of losing you.
Did you contact him first, online? I did with my DH, because I was immediately struck by his photo. I just fancied the arse off him. He turned out to be a horrible, aloof, cocky, unemotional twunt. Next time, I'm only going to go out with men who contact me first, so the wind is blowing in that direction IYKWIM.
Careful...