I think you have nothing to worry about. If guy messages you then he is interested in your personality. If Im not into girl in any way I lose patience after first 10 messages if shes not ready to meet. What you feel is normal cause chatting with someone is easy but actually meet the person takes a jump. I mean you just have to stop thinking and jump. Just like most girls likes chubby guys, most guys likes chubby girls too. 40 extra pounds is still very sex. Much sexier than none extra pound at all. Those thin girls all look the same to be honest.
I once met a girl who looked much bigger than in pictures. Few seconds of feeling repulsed and then I got over it. Girl was nice to talk to and that compensated those few seconds 1000 fold.
So thats the worst that can happen to you - few seconds of disapointment from a guy. I mean now you really are testing the guy by not meeting cause you are saying he is not good enough by holding back to meet. Thats how we guys feel about it. Yes you feel insecure but dont your insecurity kill him.
First few times meeting someone from internet feels like a jump but afterwards you get more confident in your looks and meeting just feels natural. Talking from experience here.
Best you can do is tell guy when you have time to meet now. Also if you feel insecure you could tell him and Im sure he will support you. Or if you feel nervous at a date then you could tell that its your first time meeting someone like that from chatting and that should make you feel better too after you say it.
I remember first girl I met from dating site - I was so nervous and couldnt say much. Was sure that after I been so quiet and reserved she wouldnt want to meet again cause we chattet so much and so good before. But I played it smart and didnt talked about meeting again after we met. I kept chatting with her only less and eventually she was the one to suggest to meet again. Second, third and fourth time was at her place, netfix and chill, kissing and all the nice little things thats brings two people closer. She was the one who started kissing cause I was sitting in the corner of bed scared and shy. Great memories. After that things with other girls just became easier and easier.
Doubt kills more dreams than failure ever will