take sick, fatigue
瘁 centers on a state of being worn down: falling ill from overwork or suffering deep fatigue. The two given meanings are closely linked as physical breakdown from exhaustion.
瘁 combines 疒 (sickness) with 卒, which likely contributes the sound and may suggest a sudden collapse or ending, fitting the idea of becoming sick from exhaustion.
The sickness enclosure 疒 wraps around 卒, which looks like a person collapsing. Picture someone suddenly falling ill from overwork, their body giving out from fatigue.
For スイ, imagine a person so tired they can only sip water weakly: sip -> スイ, and the sickness enclosure shows they are ill from fatigue.
giving one's all to