Lately I've been a bit sleep-deprived because I'm busy.
彼は少し太り気味だ。
He is slightly on the heavy side.
彼は緊張気味に話した。
He spoke in a slightly nervous manner.
がち also means 'tends to' but suggests a habitual or frequent occurrence, while 気味 (ぎみ) points to a slight, often momentary tendency or state.
傾向 is a full noun meaning 'tendency' used with 〜の傾向がある, whereas 気味 (ぎみ) is a suffix attached directly to a noun or verb stem to mean the same thing more casually.
がち suggests a stronger, often negative, recurring tendency, while ぎみ describes a milder, more subjective feeling or slight tendency.
気味 attaches to nouns to mean 'a slight tendency toward' (often something negative like 疲れ気味), whereas がかる describes a thing taking on the visual or stylistic quality of another noun.
気味 attaches to nouns or verb stems to show a slight internal tendency or feeling (疲れ気味 'a bit tired'), whereas めく focuses on an outward, perceptible appearance or mood taking shape.
Written identically as 気味, the きみ reading is a noun meaning 'sensation' or 'feeling', while ぎみ is a suffix meaning 'tending to' or 'slightly'.
slight cold; touch of a cold
reek of desperation; feeling of desperation
half-joking; somewhat joking; in a jocular vein
a bit overweight; tending toward plumpness
somewhat puzzled; a bit baffled
somewhat flustered; looking a bit dismayed
somewhat excited; a bit agitated
tending to anemia; somewhat anemic
From 気 (き, 'spirit; feeling') + 味 (み, 'taste; flavor'), originally meaning 'a touch of feeling'. The reading shifted to ぎみ due to rendaku.
overheated; hyper-; overearnest
somewhat reserved; a bit shy; tending to hold back