Basic Trope: A character (or ability) that starts out comparatively weak but becomes much stronger after leveling up.
Straight: When Bob joins the party, he's practically useless. After training him up, he becomes one of your most powerful characters later in the game.
Exaggerated: When Bob joins the party, he does 1 damage and dies in one hit. One hundred levels later, he becomes a Game Breaker that one-shots every enemy, is immune to everything, always attacks first, and has special powers that give you extra money and items from enemies.
Downplayed: When Bob joins the party, the only real damage he can do is by his basic attacks, his special attacks being weak. Once leveled up, his specials are cheaper but just as powerful as other characters.
Bob has a lot of potential, but is just inexperienced and needs training to unlock that potential.
Bob is untrained in actual combat, but he has studied a lot of theory, making him the smartest member. As he levels up he finds more ways to put theory into practice, ending up a balance of knowledge of magic and fighting with strength and skill that lets him use it.
Subverted: Bob joins as a weak character. You train him up, and he gets much, much stronger... only for a new game mechanic to be introduced that makes Level Grinding worthless and he's the worst at using it.
Double Subverted: Bob joins as a weak character. You train him up, hoping he'll become stronger later... nope, he's still weak... except against That One Boss, which he has a special power that takes him down quickly. Guess Bob became a Lethal Joke Character.
Parodied: Every bad guy is scared of the weakest character in the party because they think he'll eventually become the most powerful being alive.
Zig Zagged: Bob's usefulness varies wildly depending on his level, the location, and how far in the game you are.
No character joins your party as a weakling.
Weaklings stay weaklings.
Enforced: A Magikarp Power is included in a game for balance purposes.
Lampshaded: "Oh, he may be weak now, but in games like this, the weak ones always grow to be the most powerful."
Invoked: The main character purposely recruits the seemingly-weakest member of a fighting group, banking on the possibility that after some training, he will grow to be the strongest member of his team.
Exploited: The party forces Bob to stay back and watch in battles.Some battles later they lean back and let Bob charge in, knowing that he can easily kill them alone.
The villains realize that, however weak Bob seems to be, he will become much more powerful later on, so they kill him off early.
Bob never participates in battles because he doesn't want to become stronger than the others.
Discussed: "Everyone has to start somewhere. Train yourself with us and I'm sure you'll become as strong as us, if not stronger."
Conversed: "I know Bob seems useless at first, but if you train him up, he'll be really good."
A breakdown of the game mechanics shows that, while Bob might be the strongest character in the game, all the Level Grinding needed to train him outweighs his usefulness later in the game, so players instead stick with the less powerful characters that are more easily trained.
The main character never bothers to bring him/her on the journey due to how weak he/she his, never knowing that he/she will eventually become a very strong and worthy ally.
Reconstructed: Players still use Bob, despite outcries of "Stop Having Fun" Guys, because dang, it's fun to watch that once-weakling of a Bob wipe the floor with enemies. It makes all the effort put into it feel worthwhile.
Back to Magikarp Power. It'll get better the longer you stay there, I promise.