[noun] + 気味 [verb ます-stem] + 気味
気味 (ぎみ) goes straight after a noun or a verb's ます-stem and means "a touch of", "a bit": the state has started to show but is not full-blown. It almost always describes something unwelcome – health, tiredness, a schedule slipping.
The verb goes in the ます-stem, not the dictionary form: ×疲れる気味, ×下がる気味.
気味 behaves like a noun. Before another noun it takes の; to describe how something is done it takes に; with だ or です it ends the sentence.
The same characters read きみ in きみがわるい気味が悪い mean "creepy". That is a separate word, not this suffix.