If Torkoal and Weezing both come out at the same time (the start of the battle, probably, or following a double KO), then Neutralizing Gas fires first and silences Drought before it can do anything.
If Torkoal has already come out and set Drought, with Weezing arriving later, Drought has no further effects to suppress (its only effect occurs at the moment of entry, or right after an ability change that causes a Pokemon to obtain Drought) and the sun will remain in effect for as long as it's supposed to. However, if sun is already in effect, someone sends out a Pokemon such as a Cloud Nine Drampa, and then Weezing shows up, Neutralizing Gas can usefully neutralizing the ongoing effect of Cloud Nine, so the effect that masks the weather will no longer be in force, and the sun's effect will once again shine through until it's scheduled to run out.
