drag, tow, haul, delay, prolong
拖 centers on pulling something along, often with resistance or over time: dragging, towing, or hauling. The delay and prolong senses extend naturally from the idea of something being drawn out or slowed down.
拖 combines 扌 (hand) with 㐌, which likely contributes the sound and may relate to the idea of pulling or extending. The exact historical development of 㐌 is uncertain.
The hand radical 扌 beside 㐌 suggests a hand pulling something heavy. Picture a hand dragging a stubborn object that resists, causing delay.
For タ, imagine a hand tugging a heavy load: the tug sound cues タ, and the hand drags it along.