weight down vs burden

weight down is not a noun while burden is a noun.

Word	Noun	Adjective	Verb	Adverb
weight down	No	No	Yes	No
burden	Yes	No	Yes	No

As verbs, weight down and burden are synonyms defined as:

Other synonyms of weight down include burthen, weight.

weight down (noun)	burden (noun)
	weight to be borne or conveyed
	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

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