Jimmy spent a lot of his childhood on his own with only scouts to rely on. When he moved to South Park he expected the same. So when he did move and had his friends he was happy.
His fight with Timmy as what hurt him the most. (Not counting physically.) He didn't care what others thought after that he just wanted to be friends with Timmy.
Yet somehow he found a way to get on Timmy's good side. Maybe it was the fact it Jimmy realized Timmy wasn't all that bad. Maybe he was just tired of being mean.
No one knows why but they learned that Jimmy's childhood being sad made Timmy and him very close. Close enough they grew closer and closer until they fell in love. The love spread until they were adults and moved in together.
They loved each other and it was all because of their childhood.