Baby Gonzo has an unrequited crush on Baby Piggy. While Gonzo had a crush on Miss Piggy on The Muppet Show, it was very brief, lasting only from episode 124 to episode 209. Often Piggy would react to Gonzo's obscene infatuations by screaming at him or beating him up. Though in the long run despite his oddities ad behavior, Piggy does indeed care about Gonzo.
A running gag in the series featured Gonzo finding something frightening or shocking in unexpected places (i.e. opening a door see a big monster roaring, a train coming towards him, and so on. He likewise experienced mishaps in the "Go, Bye Bye!" segments at the end of every episode.
Muppet Babies was also the first time that Gonzo suffered from an identity crisis. Although his species had been indeterminate up to that point (he was sometimes referred to as a Whatever or, more often, a Weirdo), adult Gonzo would not worry about his heritage until Muppets from Space, when it was revealed that he was an alien.