It's pointless, unless you're up against a Pokemon that's not a Fire type type or any Physical attacker for that matter. Will-O-Wisp would save you at those kinds of times. Toxic Spikes is only for stallers that stall (Umbreon with Max Sp.def and Curse just sucks) and Poison types will make all your effort for nothing and Pokemon that don't levitate and are Fire type you become useless against . Its those times you wish you had Toxic Spikes to kill them slowly and attack them at the same time. Now which one?
The Conclusion
Get rid of one of them. It's pointless keeping both.
If you keep Toxic Spikes, defensive Poison types will ruin your life by absorbing them (any poison type or tat matter) and you wasted 2 turns that you could have spent setting up, etc. But if your opponent doesn't have a Poison type on their team, You can easily set those up without any worries (seeing as Poison types aren't too common) so it seems quite tempting to set these up but you waste two turns doing that. (Personally I set up in the middle of the game to wipe out all threats for my Hazard setters).
If you keep Will-O-Wisp, Fire types and Physical attackers become a living (digital) hell. If you go up against Charizard-X, when it comes in it's still immune to both and Charizard-Ys are more common. So here, Charizard becomes a big threat (seeing as X can D-Dance ad sweep or Y can utilize Sun power to easily kill Weezing since most run Fire Blast or Heat Wave).
Suggested Moveset
Weezing @ Leftovers
252 Hp/200 Sp.def/36 Def/20 Sp.atk
-Will-O-Wisp
-Sludge Bomb
-Pain Spit
-Flamethrower
Will-O-Wisp for stalling.
Sludge Bomb for STAB (and that tiny chance of poisoning).
Pain Split to heal (kind of).
Flamethrower for steel types that make your life hell.
You can also swap Pain Split for Explosion to do a bit more damage.
This is my first long answer so I'm sorry if it was bad.
Hope I helped!
-demat