If opponent plays watcher against my student who currently has 2 might, does it stay at 1 might or go to 2 when I play a spell?

Your Ravenbloom Student will be at 2 might.

According to RiftJudge FAQ #5538, when a unit buffs itself, the buff is added to its current might value (which already includes any reductions from effects like Thousand-Tailed Watcher).

Sequence of events:

1. Thousand-Tailed Watcher is played. Its triggered ability resolves, reducing your Ravenbloom Student's might from 2 to 1 (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. You play a spell.
3. Ravenbloom Student's ability triggers and adds +1 might to its current total.
4. Calculation: Your unit's current might (1) + the self-buff (+1) = 2 might.