There is no relationship between the way a battery charges and the way it discharges for different makes of batteries. Though there is an exception in weak cells- they tend to charge faster than good batteries of the same make. What determines how long-lasting a battery can be is the battery makeup, i.e. the chemical composition of the electrolyte, electrode, and the type of reaction that produce the electrons.
The weight of a battery also has no direct correlation in performance in different battery type. For instance, lithium-ion batteries weigh much less than lead-acid batteries, but lithium-ion batteries still outperform lead acid ones.