If you keep your laptop charged it will overheat the battery and damage it.
How long does the battery last without the charger plugged in? From my own experience of keeping past laptops on charge, the battery would only last roughly an hour at 100%, if not less.
I don't think it's worth changing the battery unless you still have a warranty for that laptop.. you just have to keep it in charge and turn the laptop off every once in a while.