Generally speaking just pulling the elastic tighter on a Bobobie doesn't work because the type of elastic they use is too springy. What you want to do is buy some elastic made for dolls and restring (it's not as scarey as it sounds). Junkyspot sells restringing kits for 1/4 and 1/3 size, or you can buy the elastic from CRs Crafts
http://www.crscraft.com/ by the yard. There are other suppliers as well, but some of them are overseas so check for regular doll suppliers first. You can try your craft store, but I guarantee the stuff they sell is NOT doll quality and will be too loose to work - take this from experience!
And Almysidakay is correct - lowest temp hot glue possible.