An onomatopoeic adverb describing light, repeated tugs or pushes (e.g., giving something a couple of quick tugs).
子猫が糸をくいくい引っ張って遊んでいる。
The kitten is playfully tugging the string, giving it a couple of little tugs.
彼はドアをくいくい押して中を確認した。
He pushed the door a couple of times to check inside.
釣り糸をくいくいと引いて餌に食いつかせた。
He jerked the fishing line a few times to attract the bait.
(Archaic) To fret or brood; to worry persistently. Rare/old-fashioned use.
彼は過去の失敗をくいくいして夜も眠れなかった（文語的な表現）。
He fretted over past mistakes and couldn't sleep at night (literary expression).
(Archaic) To become suddenly angry or irritated; to flare up. Rare/old-fashioned.
その言葉に彼はくいくいして席を立った（やや文学的）。
At those words he flared up and left his seat (somewhat literary).