lift, carry
抬 centers on raising something with effort: lifting a physical object or carrying it from one place to another.
抬 combines 扌 (hand) with 台, which likely contributes the sound. The character expresses lifting or carrying by hand.
The hand radical 扌 beside 台 suggests a hand lifting a platform or stand. Picture a hand raising a heavy platform to carry it.
For タイ, imagine lifting a heavy tire: tire -> タイ, and your hand lifts it up.