You are comparing her to other Kage's which is not determining where she stand as a Kage in general. You say she is the weakest, but your opinion is not back-up with logical or from the Manga. This is basically a Vs. Thread. Everyone else already gave their reasons of why she is not weak. I'll leave it at that, but... A few:
She is an Hokage. Before she became a Hokage she was a Medical Ninja. Her duty is not on the battlefield. Her main focus is on the wounded. She develop strong Taijutsu techniques to prevent enemies from interuppt her from her Medical duties. She also mastered a Justu that allows her to breaking Medical Rules.
Madara and Five Kage Battle: She healed the Hokage when they were wounded. Madara himself consider that she would be a problem, but after Oonoki come into picture, Madara worried more as he was more experience than the others. However, without Tsunade, the Kage have no chance of surviving against Madara.