I don't really carry around a concept of how much "health" my characters have in a fight, so I try to keep my type advantages a little more subtle and grounded than "this attack hurts me twice as much as other attacks do." A fire attack's effects on a grass type are clear, but, for instance, maybe a water attack makes it harder for a fire type to use fire-based attacks, or maybe it saps their energy away more than it would for someone else. (Ever try jogging while wearing a jacket soaked with water?) Maybe bugs, darkness, and ghosts make it hard you, a psychic type, to focus on your attacks.
On a related note, I like to run on a policy of "Pokemon can learn four explicit moves, and then can also freely do anything their biology or types imply." No pokemon needs to use up an imaginary move slot on Scratch, no fire type needs to know a special move to set things on fire, but if a move feels more like a technique, or it lies outside their expected skillset (usually because of a type mismatch), then I mentally tally that against the imaginary four-move-limit.