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)’.

• 最近（さいきん）太（ふと）り気味（ぎみ）だから、ダイエットしなきゃ。
  I feel slightly fat, so I should go on a diet.
• 今週（こんしゅう）は色々（いろいろ）と忙（いそが）しかったから疲（つか）れ気味（ぎみ）だ。
  Because I have been busy this week with various things, I am feeling a little tired.
• 今朝（けさ）は風邪（かぜ）気味（ぎみ）だったので、学校（がっこう）を休（やす）んだ。
  Because I felt a little sick this morning, I took a day off of school.

ぎみ 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.

• 現場（げんば）の人（ひと）がほとんどバテ気味（ぎみ）だったので、作業（さぎょう）を中断（ちゅうだん）した。
  Most of the people on the site seemed a little worn out, so we stopped work.
• 電車（でんしゃ）が遅（おく）れ気味（ぎみ）だから、待（ま）ち合（あ）わせ時間（じかん）まで間（ま）に合（あ）わないかも。
  Because the train seems a bit late, I might not be able to make it by our agreed time.
• 風邪（かぜ）気味（ぎみ）なのかな？身体（からだ）がだるい。
  I feel like I have a cold, my body feels heavy.

As ぎみ expresses ‘weak signs of (A)’, it is often used to soften a statement, so that the speaker does not appear overconfident.

• タカシ君（くん）疲（つか）れ気味（ぎみ）じゃない？ちゃんと休憩（きゅうけい）取（と）った？
  Takashi-kun, you look a bit tired, did you take a proper break?