"a summer resort...encumbered with great clapboard-and-stucco hotels"- A.J.Liebling; "a hiker encumbered with a heavy backpack"; "an encumbered estate"
is similar to
bearing a physically heavy weight or load
"tree limbs burdened with ice"; "a heavy-laden cart"; "loaded down with packages"
is similar to
loaded with something that hinders motion
"The wings of birds were clogged with ice and snow"-Dryden
is similar to
entangled or hindered as if e.g. in mire
"the difficulties in which the question is involved"; "brilliant leadership mired in details and confusion"
is similar to
burdened with legal or financial obligations
"his house, his business, indeed, his whole life was heavily mortgaged"