I like to write letters to friends whom I still care about but no longer talk as often, or if they live kind of far away. They usually write back, and from there I like to start a letter chain with them.
Am I apparently burdening people by doing this? They usually take a month or two to write back, and I usually write back within a week at the very least, two or three at most.
It's not a burden. I think anyone would enjoy a handwritten letter. If the truly were bothered by it, they would tell you or just not write back.