Gambit did not love the woman Sabertooth killed. What happened was Gambit had to steal some fancy necklace, I forget the name of it from this very attractive young women who stole it herself by seducing the original owner. Gambit stole it the same way, by getting the lady to fall in love with him. Sabertooth was hired by the original owner to get the necklace back and what he did is took the woman and Remy's brother and tied them up, held them over the edge of a huge building. Sabertooth dropped both of them knowing that he could only save one of them, he saved his brother and the woman fell to her death. Gambit went down to her and as she was dying she told him that she loved him and would have given him the necklace freely if he had just asked. Sad, and that was Gambit's initiation into the Theive's Guild (stealing the necklace)
Another reason Gambit hates Sabertooth is that after going into debt to Sinister, Gambit was assigned a job with Sabertooth (before the whole necklace thing I think) and that just so happened to be the job that led to the mass murder of the morlocks, Gambit did not know that the intentions were to kill them and was able to save Marrow when she was a child, Sabertooth tried to kill him during this whole dispute too.
Also, Sabertooth tried to use his knowledge of this whole morlock thing as leverage against Gambit, even hinting to Rogue once about it. Gambit hates Sabertooth because of these reasons, also because Sabertooth is the most heartless, evil, sick villian out there, I've read his series (well the first ones) and there is not a good natured bone in his body, this was not very well represented in the movie, Sabertooth is all about making the world misserable just for the sake of doing it.
Aww, maybe he did love her, see, Gambit's not that bad, you kind of like him don't you Pr? Yeah, Sabertooth is sick, he has his own series and there is nothing nice about him, he's probably the worst, I mean, Sinister and Apocolypse, Magneto, all those guys have some kind of motive but Sabertooth is just evil and that is one big reason Wolverine hates his guts, there is no hope for him.
Oh, I thought there was something you wrote once or something you implied that led me to believe you were not fond of Remy. Hmmm, maybe just my imagination. No, I think I'm right actually. It was one of the first 'virtual conversations' (cute, non?) that we had, you and I, something, something, something...