Despite how much I've drawn of Adult Barclay he's still technically a little baby in canon and I'll be elaborating only on canon happenings so far here.
Left home and his mom (Sparrow) to find work because he really needs the money. He had a happy life with his mom and still keeps in touch but there's things he wants to save for, and joining the Palette was the best way to do that.
He was assigned the name Blush and was partnered up with Copper. They had a rough patch at the start and ended up stressing eachother out a lot.
They're figuring things out now and getting used to living/working with a stranger.
Barclay is a grumpy and stubborn kid if he's put off but he has a really good heart and is capable of being funny and warm and kind as well. He's slow to open up to people if he doesn't feel respected or taken seriously.