heavily
lightly
slightly
casually, comfortably, lazily, nonchalantly
Kate leaned comfortably against the wall.

eagerly
confidentially, conspiratorially
weakly, wearily
precariously
close, near
He leaned closer, lowering his voice.

across, down, forward, out, over
She leaned forward eagerly to listen to him.

away, back, backwards/backward
He leaned back in his chair.

sideways

across
She was leaning confidentially across the table.

against
She leaned her head against his shoulder.

from
Women and children leaned from the windows of the surrounding tenements.

into
He leaned into the open doorway.

on
The old man was leaning heavily on a stick.

out of
She leaned precariously out of the window.

over
She leaned casually over the railings.

through
The taxi driver leaned through his window.

to
She leaned to one side.

towards/toward
He leaned towards/toward her.

heavily
Britain leans heavily on Europe for trade.

Lean is used with these nouns as the object:
back, chin, elbow, head

Lean is used with these nouns:
bacon, beef, body, build, cut, face, figure, finger, frame, ham, hip, meat, muscle, period, physique, spell, steak, turkey, year