put off, procrastinate, endure
捱 centers on delaying or resisting an action or hardship: putting something off, procrastinating, or enduring a difficult situation without giving in.
捱 combines 扌 (hand) with 厓, which likely contributes the sound. The exact historical development is uncertain, but the hand component suggests an action of holding back or pushing away.
The hand 扌 beside 厓 (a cliff-like shape) suggests a hand pushing against a cliff, either holding it off or enduring the pressure.
For ガイ, imagine a guy procrastinating by leaning his hand against a cliff: guy -> ガイ, and he keeps putting off the climb.