If my opponent plays Bellows Breath to bring a unit to 3 might, then plays Thousand Tailed Watcher, does the unit die?

Yes, the unit will die if its Might is reduced to a value equal to or less than the damage marked on it.

Here is the breakdown of how this interaction works:

Sequence of Events

1. Bellows Breath: Your opponent plays Bellows Breath. It deals 1 damage to your unit (or 2 if they paid the Repeat cost). This damage is "marked" on the unit.
2. Thousand-Tailed Watcher: Your opponent plays Thousand-Tailed Watcher. Its "When you play me" ability goes on the chain.
3. Resolution: The ability resolves, applying -3 Might to your unit (to a minimum of 1 Might).
4. Cleanup: After the ability resolves, the game checks the unit's status. If the damage marked on the unit is equal to or greater than its current Might, the unit is killed.

Key Rules

• Damage vs. Might: According to FAQ #2141 and FAQ #91, damage is "marked" on a unit and does not reduce its Might. A unit dies when the marked damage equals or exceeds its current Might.
• Might Reduction: The -3 Might from Thousand-Tailed Watcher lowers the unit's Might threshold. If the unit had, for example, 4 Might and 4 damage marked on it after the Watcher's ability resolved, it would die because its Might is now 1 (or 4, depending on the original Might), and the marked damage meets or exceeds that value.
• Timing: As established in FAQ #3100, you cannot prevent the Thousand-Tailed Watcher's ability from resolving by killing the unit in response; the ability will still resolve even if the Watcher is removed from the board.

Summary: The unit dies because the Thousand-Tailed Watcher reduces its Might, making the previously marked damage from Bellows Breath lethal.