Can Bilgewater Tracker deal 1 damage twice to the same unit?

No — Bilgewater Tracker's "deal 1 to each of up to 2 units" picks a group of at most two units, so a given unit can only be chosen once and only takes 1 damage.

"Up to 2 units" is a choice of targets from the available units (Rules 355.13, 355.9) — you may pick two different units or just one, but you can't pick the same unit twice to stack the damage. That's different from cards worded as two separate instructions, like Falling Star's two "Deal 3 to a unit" instances, where pointing both at the same unit is legal (and charges its Deflect twice, FAQ #12966).

So to kill a 2-Might unit you'll need a second damage source; the Tracker alone will only ever mark 1 on it.