They are conjugates to each other. So for example HCl -----> H+ + Cl-
HCL is a strong acid and dissociates into the acidic H+ proton and the conjugate weak base of Cl-. The conjugate of the Cl- would be the protonated form as HCl. As far as knowing if something is weak, its pretty simple to memorize all the strong acids and bases, most chem textbooks have them. I believe another rule of thumb used is if the Ka or Kb is less than 1 it is considered weak, whereas if it is over 1 it wants to go to completion more. I'm pretty sure this is right... anyone able to back me up? Haha