If Watcher reduces the might of something to 1 (but the unit is only -1 from being at 2 originally) then the unit gets +2 from Wuju Bladesman, does the unit go up to 3 or stay at 1 because Watcher's full -3 is now in effect?

To answer your question, we must look at how Thousand-Tailed Watcher's ability interacts with subsequent might buffs.

According to the official rules and FAQs for Thousand-Tailed Watcher (such as FAQ #8931), the effect does not create a static lock at 1 might. Instead, when the ability resolves, it snapshots the actual amount of might it reduced the unit by as a modifier for the rest of the turn, while respecting the "minimum of 1 might" restriction.

The Calculation

1. Watcher Resolution: Your 2-might unit is targeted by Thousand-Tailed Watcher. The effect calculates the reduction: 2 - 3 = -1. Because of the "minimum of 1" restriction, the unit's might becomes 1. The game "snapshots" this reduction as a -1 might modifier for the rest of the turn.
2. Buff: You apply a +2 might buff from Wuju Bladesman.
3. Result: The calculation is: Base Might (2) + Buff (+2) + Snapshotted Modifier (-1) = 3 Might.

Summary

The unit will go up to 3 might. Thousand-Tailed Watcher applies a persistent modifier that persists for the turn; it does not "increase" its reduction to -3 later in the turn if a unit's might increases. Subsequent buffs are applied normally to the base might and the already-calculated modifier.

This is my interpretation based on the official rules for arithmetic effects (Rule 472.3.d) and existing FAQs (FAQ #8931) for Thousand-Tailed Watcher. No official FAQ exists specifically for the interaction with Wuju Bladesman, but the mechanic follows the established rules for snapshotting modifiers.