Yeah, the advancement system in FFII is weird that way...they could've executed it a bit better to prevent stuff like this.
Besides beating up your own people, you can do the Attack/Cancel trick to raise your weapons and spells' levels. Just select a target with an attack or spell, and then cancel. Re-select a target, and cancel again. The proficiency of that weapon/spell will go up 1 point for each time you re-target/cancel, regardless of if you actually used it or not. This'll work for everyone but the fourth member of your party (who you usually don't bother to train extensively anyway, except Leon.) This won't work in the Gameboy Advance version.
Another way to increase your HP/MP is to use the magic spell, 'Swap'. (Or 'Change' in some versions.) Use this on the weak vine enemies near the first town (or the enemies inside the Semitt Falls Cave if the world map encounters have changed yet), and since your HP and MP have gone down to the level of the weak monsters, your HP, MP, and various other stats will be raised, just from one battle! Unfortunatley, you'll be weakened and out of MP, and you can only get Swap in Mysidia, which is very far into the game. This trick works in all versions of the game.
Of course, you'll have to level it up some to make it successful most of the time, but it doesn't take too long to max out all your characters HP/MP this way, and it really makes the menu screen look awesome with maxed out stats. xD Of course, some initially melee fighters like Guy/Gus may have a hard time using their brain to cast a spell.