It's obviously not out of love for Britain, so am I missing something important? Did it obstruct the power of Quebec as a province in some way? Did it somehow weaken the sovereignty movement?
One key element was how it was accomplished, and in particular the events which occurred during the night of the 4^th November 1981. That night, all premiers met with the prime minister in the kitchens of the Chateau Laurier in Ottawa and agreed to the Constitutional act to rapatriate the constitution. All of them, except the premier of Québec, that is. The Québec premier was lodged in Hull for those talks, across the Ottawa river, and he had specifically asked to be called if something substantive occurred when he retired for the night. When this discussion happened, he was not invited. Because of this, the agreement was built without addressing the specific constitutional demands of Québec, which was seeking special powers to protect its unique french culture. When then premier René Lévesque learned in the morning that an agreement had been negotiated and finalized without him, he took it as a slap in the face, refused to sign it and left the meeting in outrage. This event is referred to as "the kitchen meeting" in english Canada, but as "the night of the long knives" (Nuit des longs couteaux) in Québec.
To this day, the name of Pierre Elliot Trudeau is reviled by many québécois because of those events.
This set the stage for the following 30 years of Québec/Canada relations, the eventual foundation of the Bloc Québécois, the separatist Parti Québécois maintaining itself as one of the two main parties in the province, and the 1995 referendum.
For more info, you can look up these:
http://www.lactualite.com/politique/1981-longs-couteaux-la-vraie-histoire/