be in great difficulty, greatly
殢 centers on being stuck in a difficult, exhausting situation. The given meanings "be in great difficulty" and "greatly" suggest a state of extreme hardship or weariness.
殢 combines 歹 (death, decay) with 帶 (belt, sash), but the exact historical development is uncertain. It may have originally expressed a sense of being bound or trapped in a deadly situation.
The left side 歹 suggests death or decay, and the right side 帶 looks like a tangled belt. Picture being tied up in a decaying, impossible situation—great difficulty.
For テイ, imagine being in such great difficulty that you can only manage a weak "tay..." sound: tay -> テイ, as you struggle to speak.