The equipment the character has when they level up directly affects the stat increases. For instance, if you level up with equipment that raises a character's Strength, they will gain more HP when they level up. Similarly, if you level up with equipment that raises a character's Magic, they will gain more MP when they level up.

Originally Posted by
Pure Quin14
So the mages have little HP because they can take less damage, whereas the melee fighters need more because they're right at the front lines.
This isn't entirely true. If you level up 98 levels with maximum Strength increase, Dagger, Eiko and Freya will have the same HP.

Originally Posted by
drunkymonkey
Mages aren't meant to have much HP are they? That's Steiner's job.
Steiner's HP isn't much higher. Amarant, Beatrix, Blank and Zidane have more HP than Steiner. Marcus and Quina have the same HP as him.