Melodrama, as a genre, was a staple of Victorian theater. It took on a negative connotation when electric lights were introduced and the stages were brightly lit. Actors no longer had to use such dramatic makeup or exaggerated gestures.
There is more in what people don't say than in the words they speak. Make sure your dialogue isn't on the nose. Imbue it with subtlety and nuance. Avoid lecherous pronouncements, grandiose speeches, and "as you know, Sally" dialogue.
Your verbal camera moves in close when a character is speaking and reacting. It picks up intimate body language. Use it judiciously. The smallest gesture can speak louder than shouting or punching a wall. Avoid wiggling eyebrows, stroking mustaches, and rolling eyes.