I think it depends on how you define "weak". Like, I'm physically weak but I believe I'm mentally strong. Not as strong as I'd like to be. My anxiety is VERY bad and I don't have the greatest self-esteem, but I'm very strong-willed. I'm very critical and not easily influenced. Also, I can fight to the death if I have to. This is me and I am not a sign. I'm just trying to illustrate how definitions of strong vs. weak can differ.
I think every sign can be seen as strong/weak in it's own way. I'm not saying this to be nice. I have no reason to be nice. I'm talking about the signs as archetypes, not people, but take a sign like Pisces for example. Pisces could be seen as weak: impressionable, easily influenced, oversensitive but as Sibylline said, Pisces is strong in empathy and imagination.
Then on the opposite end, we have strength. When I think "strength", Aries (representing the warrior archetype) is the first sign that comes to mind. Pisces is stereotyped as oversensitive but Aries is stereotyped as easily angered and that could be seen as oversensitivity too, in a way. If you're the type to get angry at every little thing, that too could be seen as a weakness. This could be perceived as childishness or immaturity. Impulsiveness isn't always the most intelligent option, and sometimes, it takes real strength to admit your vulnerability rather than trying to win at everything. I'm talking about Aries as an archetype and mostly just it's shadow side, not Aries Suns.
It sickens me to see weakness in others, because I hate to see it in myself. I think it's mostly the Scorpio in my chart that makes me this way, but the Taurus and Uranus might also have some effect. Even the Libra...I see myself as being the archetype of the judge, "objectively" weighing every piece of evidence there is…I can't trust other people to make decisions for me. Decision-making is MY strong suit, even if they take a while to form. I would define strength as the ability to think for yourself, but other people would define "strength" differently (...one of my teachers believes that freethought is a negative consequence of America capitalism...). In this case, I would assume Sagittarius to be the "strongest" sign, at least as an archetype…in my experience, Cancer Suns (especially with Mercury and Venus in Gemini) happen to be the "weakest" (according to my own definition), but I don't think Cancer is weak as a sign. Cancer is known for having a hard protective shell, and then there are individuals such as Courtney Love whose strength I admire.