He probably gets naked at parties because at least that way he gets attention. Id imagine day to day he doesnt attract much female attention or is just known as 'the fat kid'. He probably feels that people are laughing with him rather than at him when this happens and just feels happy to have 'friends'.
And id imagine that he has such little female attention in the past which explains his quite worrying displays of love. Getting attached that easily is probably more out of desperation than anything else and i would imagine he is lonely.
He obviously has an issue with weight. Going from 24 stone to 18 stone is not an easy task (as someone who has done it - its very difficult) Life is a lot more difficult when youre very overweight. And its a shame that he put it back on, which is very easy to do when you have issues with food. But he has the knowledge to do it again, all he needs is the willpower.
Im fairly certain he already KNOWS why he doesnt have a girlfriend. Its as obvious to him as it is you, he has to look in the mirror at himself every day. And as he appears to be so sensitive I dont believe telling him straight would be a good idea.
My suggestions would be:
Do you ever speak to his parents? His parents encouraging him to lose weight would probably benefit him a lot more than his friends telling him to do so. I doubt he wants to be thought of as 'different' by his friends. If a parent suggests it, it will come across in a more caring manner rather than his friends digging at him.
Alternatively, are there any other big guys you are friends with. Its unlikely that if you tell a 26stone guy to go to the gym that he will go alone and have a beneficial work out. Also. if you send him along with someone much fitter then that will just embarrass him. If you could pair him up with another big guy then its both encouraging and competitive.