Another way to consider it might be that rather than considering Ophelia weak, I think the house of Denmark is filled with people who have mental issues of a varying degree. Viewed in that light, Ophelia isn't necessarily weak, but rather someone who desperately needs help from a family figure in a position to do so, perhaps as a mother might do. She has a brother, but he's understandably confused and occupied with the events in front of him. Gertrude has her own issues, as does Hamlet, and of course Hamlet makes the entire situation worse.
Overall, I think you can take the most strong willed person and break them down through events that unfold around them. True, a weaker person might fold faster, and in spectacular fashion, and both of these points are shown by Ophelia. I think she does kill herself out of despair, and when Gertrude describes her death, knowing her mental state and behavior helps to diminish the value of whatever it is that she has to say.
I agree with malibrarian; Ophelia is a long way from the strongest female that Shakespeare has given us, and I think that helps us see her as weak.
I think if we judge her by 21st-century standards she will definitely come up looking weak. But if we consider the times in which Shakespeare wrote, we may end up being more sympathetic to her plight. She was doing her best to obey her father and her older brother - the two people in the world who had complete control over her present and future (other than the king and queen). It may have been heart-breaking, but she was told to cut ties with Hamlet, and so she did (not knowing, of course, that she was a pawn for Polonius and Claudius to use to see what was the matter with Hamlet).
Many people will look to her "suicide" as reason enough to label her weak. The text does not explicitly say she committed suicide, although the priest at her funeral claims she did, which means he won't allow any further ceremonies to be done for her (much to the chagrine of brother Laertes). But Gertrude's description of her death sounds more to me like Ophelia just was so out of reality that she did not realize the danger she was in when she was in the water.
Ophelia is definitely not as strong-willed as many of Shakespeare's female characters.