Collocations for weary - adj.

be, feel, look, seem, sound
become, get, grow
I've grown rather weary of all your excuses.

make sb
This war has made us all weary.

extremely, fairly, very, etc.
a little, slightly, etc.
She looks a little weary.

of
The people are weary of war.

Weary is used with these nouns:
bone, brow, cynicism, eye, limb, mind, resignation, shrug, sigh, traveller