Let's say I have a 2 might unit and my opponent plays Thousand Tailed Watcher. My unit becomes 1 might. If then, afterwards during that turn I use a +1 might pump spell, does my unit become 2 might, or does the Watcher trigger keep reducing all might up to a total of -3 down to 1?

Based on the rules and FAQs for Thousand-Tailed Watcher, your unit will become 2 might.

Ruling

When you play a +1 might pump spell on a unit already affected by Thousand-Tailed Watcher, the unit's might increases normally. Thousand-Tailed Watcher does not create a static "lock" at 1 might; rather, it applies a modifier that snapshots the amount it reduced the unit's might by at the time of resolution.

Sequence

1. Watcher Resolution: Your 2-might unit is targeted by Thousand-Tailed Watcher. The effect calculates the reduction (2 - 3 = -1, capped at a minimum of 1). The effect "snapshots" this reduction as a -1 might modifier for the rest of the turn.
2. Pump Spell: You play a +1 might pump spell.
3. Calculation: The game applies the base might (2) + the pump (+1) + the snapshotted modifier (-1).
   • 2 + 1 - 1 = 2 might.

Supporting FAQ

According to the FAQ regarding this specific interaction:

"Watcher applies a -1 might modifier for the rest of the turn (limited by the minimum of 1 might). Subsequent might increases are applied normally to the modified value."

This is further clarified by Rule 454.3.b, which explains that when an arithmetic effect has a limitation (like "minimum of 1"), it is limited at the time of application and "remembered" (snapshotted) at that limited level for the duration of the effect.