As adjectives the difference between haggard and weary
is that
haggard is looking exhausted, worried, or poor in condition while
weary is having the strength exhausted by toil or exertion; tired; fatigued.
As a noun haggard
is (dialect|isle of mann|ireland) a stackyard, an enclosure on a farm for stacking grain, hay, etc.
As a verb weary is
to make or to become weary.