Considering that Weavile doesn't learn U-turn, Ambipom is the better option, but even if it did, Ambipom would still be the superior choice.
Ambipom's technician ability allows it to hit stronger with fake out, and while it does not get STAB on fling like Weavile, it can take advantage of not having an item by running acrobatics to cover fighting types. Speaking of which, Ambipom's one weakness to Weavile's six and similar bulk make's Ambipom the superior option. Additionally, Ambipom can take adavantage of King Rock's flinch chance with STAB Double Hit, and has a far more expansive movepool than Weavile, which is essentially limited to Dark, Ice, Fighting and Poison moves in terms of useful coverage.
Although this strategy is very gimmicky, Ambipom would do it better, and Weavile is better of with using Knock off and pursuit for mind games and Ice Shard for revenge killing
Hope this helps