The heart 忄 beside 亡 'perish': busyness as the heart's small death. The etymology is practically a public-health warning — when every hour is claimed, something in the chest goes missing. Ancient scribes understood burnout.
最近忙吗？'been busy?' is the standard Chinese greeting between friends — busyness as weather. The reply 瞎忙 'blindly busy' (much motion, no progress) is the national mood of every December. 帮忙 'help with the busy' is how you ask any favor.
When the heart 忄 starts to perish 亡 — you're too BUSY.
The character diagnoses itself: 忙 = heart + death. Chinese buried a productivity critique inside its own word for busy.