Remus - your laugh. He loved hearing your laugh even though you hated it, he tries to make you laugh all the time and it never fails.
James - your attitude. James had always loved how sassy you were, it was attractive to him and when you had became friends with him, he forgot all about Lily Evans.
Sirius - your loyalty. Loyalty was very important to Sirius, especially that his own family disowned him and all he had was the Potters. After Lily and James had been murdered and he was sent to Azkaban, you always knew eventually you'd meet again. Once he escaped, he came looking for you. You hadn't moved on and was happy to start a new life with him on his release.
Peter - your wit. He loved your cleverness and good sense of judgement. He admired your perception of everything and wished he could be as sharp witted as you are.