WGC doesn't give the Thalmor absolute power, they actually do things in secret while the Empire suspects they're up to something. They don't have proof, but the Thalmor to make an open arrest need proof to touch an Imperial Citizen, this is seen in Markarth where the Thalmor ask you to find proof of Talos worship. The WGC has been in place for nearly thirty years, the issues with the Thalmor are only recent with the rise of Ulfric Stormcloak, the treaty was poorly enforced and many Nords didn't even care, they all still had shrines to Talos.
"We didn't pay much attention to it when I was a boy - everyone still had their little shrine to Talos. But then Ulfric and his "Sons of Skyrim" started agitating about it, and sure enough the Emperor had to crack down." - Alvor
The Empire knows they're up to something, the Stormcloaks don't even know they're doing what the Thalmor want.
Tullius:
"You realize this is exactly what they wanted."
Galmar:
"What who wanted?"
Tullius:
"The Thalmor. They stirred up trouble here. Forced us to divert needed resources and throw away good soldiers quelling this rebellion."
It is interesting to see people hate on the Empire for killing three people and ordering your execution. When the Stormcloaks sack and burn two cities and kill more Nords than the Legion and Thalmor combined.
They admit to it in their Dossier.
The incident at Helgen is an example where an exception had to be made - obviously Ulfric's death would have dramatically increased the chance of an Imperial victory and thus harmed our overall position in Skyrim. (NOTE: The coincidental intervention of the dragon at Helgen is still under scrutiny. The obvious conclusion is that whoever is behind the dragons also has an interest in the continuation of the war, but we should not assume therefore that their goals align with our own.) A Stormcloak victory is also to be avoided, however, so even indirect aid to the Stormcloaks must be carefully managed.
While both sides victory will harm Thalmor plans, the Empire victory harms them in the future, Stormcloak victory only harms their agents within Skyrim who are behind enemy lines. Though they do aid the Stormcloaks in fighting the Empire, Windhelm is broke so someone is funding the rebellion. Windhelm's stockpiles are empty from Ulfric's useless management. His city has fallen into disrepair and is about as poor as Winterhold just it still has walls. The Stormcloak ideology also harms Skyrim with their no buying from Non-Nords harms merchants and business within Skyrim.