Coming from the 名詞（めいし） 気味（きみ） meaning ‘sensation’, ぎみ
is a 接尾語（せつびご） (suffix) that is used to convey weak signs of (A). ぎみ
may be used with nouns, or the 連用形（れんようけい） (conjunctive form) of verbs. Often, ぎみ
is translated as ‘looking (A)’, ‘a touch of (A)’, ‘feeling a little (A)’, or ‘slightly (A)’.
I feel slightly fat, so I should go on a diet.
Because I have been busy this week with various things, I am feeling a little tired.
Because I felt a little sick this morning, I took a day off of school.
refers to the senses of the person who is experiencing them, and therefore may be used to refer to feelings about other people/things, or feelings about oneself.
Most of the people on the site seemed a little worn out, so we stopped work.
Because the train seems a bit late, I might not be able to make it by our agreed time.
I feel like I have a cold, my body feels heavy.
expresses ‘weak signs of (A)’, it is often used to soften a statement, so that the speaker does not appear overconfident.
Takashi-kun, you look a bit tired, did you take a proper break?
Although it comes from 気味（きみ）, ぎみ will always be said with a ぎ, and not a き. This is a sound change used to distinguish the noun and the suffix.