weight vs burden

weight and burden both are nouns.

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

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

As verbs, weight and burden are synonyms defined as:

Other synonyms of weight include burthen, weight down.

weight (noun)	burden (noun)
an artifact that is heavy	weight to be borne or conveyed
sports equipment used in calisthenic exercises and weightlifting; it is not attached to anything and is raised and lowered by use of the hands and arms	the central idea that is expanded in a document or discourse
the vertical force exerted by a mass as a result of gravity	an onerous or difficult concern
the relative importance granted to something	the central meaning or theme of a speech or literary work
an oppressive feeling of heavy force
a unit used to measure weight
a system of units used to express the weight of something
(statistics) a coefficient assigned to elements of a frequency distribution in order to represent their relative importance

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