The adjective form of burden is burdened. I traveled with a heavily burdened cart. (Burdened is, of course, a past participle of the verb to burden, but past participles can also be used as adjectives.)
burdened; loaded down.
of Burden
The word laden can have a number of meanings. It can mean "filled with a great quantity" such as "that table is laden with food". It can also mean "burdened mentally" such as "laden with grief".
Encumbered typically means that someone or something has been so heavily restricted or burdened that they are unable to move freely or easily. An example of its use would be: The camel was very heavily encumbered by all the luggage.
It means that you feel burdened or overwhelmed by something.
Nouns describing objects do not have opposites. "Unncumbered" is the opposite of "burdened" (if by luggage you mean something that is a burden)
Weight or pressure.
Burdened
To have walked heavily.
exhausted
Burdened