You do not have to use your weapon/spell in order to get credit for it. For weapons, select a target and when the next person's turn comes, cancel and select again. This will earn you between1-4 points, depending on the monster. Repeat for about 100 times to level up the weapon. This can only be done for the first 3 characters. If you don't have a 4th character, then it will only work for 2 characters. The same can be done for magic. Select a spell, select the target, then cancel. Again, you will earn between 1-4 (and sometimes more) depending on the monster. After you get the 1-4 points, everytime you use it after the 1st gives you only 1 point. This is a real quick way to beef up your Weapon/Magic Level, if you are willing to spend a lot of time on it.
For those of you who don't want to spend a lot of time on leveling (like myself), here is a much easier way to gradually level up your weapons/magic. Do the same as above but do it 1 time for every spell. For example, use Cure on Frioniel, then cancel, then use Life, Heal, or whatever. This is no where near as time consuming, but you will not be as powered up as the other way. The same can be done with weapons.
Easy Stat Building
Enter a battle and begin attacking your party (but don't kill them). Drop their HP a bit and at the end of a fight, Vitality and HP will go up. To raise MP, just use magic to waste your MP and you should raise your MP a bit. Use White Magic a lot to raise Soul, and use Black Magic a lot to raise Inteligence. Use your weapon multiple times during battle to raise Power. I also found that sometimes Agility raises by using the Run command, but it might not always work.
Easier Stat Building
What? You want an easier way to raise stats? Ok then. Get the Change spell in Mysidia and level it to around Level 5. Fight a Goblin outside near Altea (or if you already defeated the Mysidia Tower, go to the Semite Cave). Use Change on the Goblin to change stats. Your HP will drop to 6 and MP to 0. Finish the fight and just about every one of your stats will increase.
The Blood Sword may be the weakest sword in the game, but when you find one, hold onto it. The Bosses who guard the Genji equipment in Pandemonium and even the Emperor himself will take a LOT of damage from this sword, more than the Masmune even. There are a total of 2 Blood Swords found in the world.
Early in the game, right below Altea on the Peninsula, if you go close to the waters, you will fight monsters that you shouldn't see until you visit Mysidia. The monsters are worth a bit of money, if you can survive long enough. Most of them are weak to a certain element, so if your magic is high enough, you might want to try it out.
From Kashuon, if you walk directly south, you should enter a Chocobo Forest. Catch one and go outside and you can ride it without having to worry about monsters attacking.
If you level the Change spell to a really high level, it is possible to change stats on really strong bosses/monsters. The only thing I find useful for Change besides the Goblin trick is that if you run low on MP, find a monster with a really high MP total and use something like Change8 on the monster, and voila! Your MP should be full or at least better than before, and you don't have to worry about spells being cast on you.
Spells Worth Getting
In Final Fantasy II, there are many spell that are out there, but which ones are really worth getting? Here is what I think you MUST get. Cure, Heal, Life, Fire, Ice, Bolt, Aero, Holy, Flare, Ultima, and Exit. The next ones are optional. Change, Safe, Shell, Wall, Barrier, Haste, Peep, Warp, and Aura. Any other spell that changes status of the enemy is not worth getting, like Death, or Blind.