抬 often implies cooperative lifting (two or more people carrying something together) or raising something upward. 抬价 = to raise prices. 抬杠 (táigàng) = to argue for the sake of arguing.
Left indexing hand radical 扌 — left-side variant of 手. Anchors 抬 in the hand-action family alongside 提 (carry), 举 (raise), 拿 (take), 推 (push). Lifting is fundamentally a two-handed effort, the clearest of manual actions.
Right 台 supplies the sound (tái → tái, identical). 台 itself means "platform, terrace," lending a faint flavor of "raising up to a platform" — exactly the action of 抬. Same phonetic family: 苔 (moss), 怠 (idle), 殆 (nearly), 始 (begin — drifted).