Burthen is simply an old way to write burden: a heavy load, or something hard you have to carry, including duties and worries. You may still see it in old poems, older Bibles, or sailors' talk — a ship's burthen was how much cargo it could take. Nobody writes burthen in a normal school essay today unless they are copying old language. There was an old verb too, with the same spelling, meaning to load someone with a burden. The th in the middle stayed in the spelling for a while, the way murder used to be written murther. In modern English, write burden and say it like burden.

負擔（burden 的舊拼）。現在作文請寫 burden。