burden vs burthen

burden and burthen both are nouns.

Word	Noun	Adjective	Verb	Adverb
burden	Yes	No	Yes	No
burthen	Yes	No	Yes	No

As nouns, burthen is a hyponym of burden; that is, burthen is a word with a more specific, narrower meaning than burden:

Other hyponyms of burden include dead load, live load, superload, millstone, overburden, overload, overload.

As verbs, burden and burthen are synonyms defined as:

Other synonyms of burden include weight, weight down.

burden (noun)	burthen (noun)
weight to be borne or conveyed	a variant of `burden'
the central idea that is expanded in a document or discourse
an onerous or difficult concern
the central meaning or theme of a speech or literary work

burden (verb)	burthen (verb)
impose a task upon, assign a responsibility to	weight down with a load
weight down with a load