The Empire is weak already. The Stormcloaks want to be free of it, to not be dragged down anymore, free to rule themselves and free to worship who they please without people disappearing and/or being handed over to the Thalmor for it. They would probably fight with the Empire against the Thalmor if the Empire wasn't trying to keep them under their thumb. As it is, the Empire only weakens themselves further by trying to forstall what I see as inevitable, a free Skyrim.
I played the Empire side my first playthrough, and didn't like it. I have played the Stormcloak side since. General Tullius isn't a bad man, imo, but just following orders isn't an excuse in my book, and no matter how much I like Legate Rikke, neither is enough for me to side with them. I don't feel the reasons are stupid, though I must be even get into another one of these threads. Sorry Sephelutis, but that's the way my characters and I see it. People can cite lore and books all they want, I am Stormcloak all the way.
There is actually very little evidence that the empire is weak, for all we know cyrodiil could be back to the way it was before the great war and we still don't know whats going on in High rock, another thing is that the kind of society that Ulfric wants to bring back is the old nordic society, the one where civil wars and tyrants were a common thing, he essentially wants to bring back the barbaric ways which for some reason some nords think is the best way to live. Another thing is that we have confirmation that Talos worship was still being practiced in skyrim before Ulfric's rebellion it just wasn't done in any chapel which shouldn't really matter right? Just as long as you worship the god you want to worship other then that there is no sign of the imperials oppressing the nords in anyway in fact Skyrim would probably be more stable under Imperial rule then stormcloak rule because while Ulfric may not be a racist there are certainly a lot of stormcloaks that are or will use their power to take advantage of a minority easily, like the silver-bloods enslaving more reachman and trying to take over all mining operations in Skyrim through use of mercenaries. Another thing is and this is shown through in-game dialogue most of skyrim's named npc population, nords and non-nords, seem to favor the Imperial over the stormcloaks, especially in Dawnstar or Riften. Really the kind of society Ulfric wants to make wouldn't work at all because its too barbaric and he picks the wrong people to lead the holds.
"We'll cleave through the legion to get to them."
This quote is funny because the stormcloaks had a hard time fighting a minor force of the legion.