Sensory Input and character's thoughts:
By itself, your "Why-yy?" works okay to deliver the verbal statement being made. It might confuse some readers, but most would get it. But you probably are more interested in delivering the emotional content of the suspicion.
It depends on your POV, but I would have gone with a description of Gemma's emotional response and her physical suspicion.
Gemma had heard this kind of suggestion from her friend Lizzy before, and the last time, her friend set her up on a blind date with Lizzy's cousin who had spent the whole time staring at Gemma's breasts. Gemma's shoulders tensed and her eyes tightened with suspicion. Her voice dropped. "Why?"
Obviously if you can't describe the character's emotional state or thoughts, the first lines wouldn't work. But using multiple senses in describing the suspicion (including the somewhat explicit inclusion of the term suspicion) gives a vivid response to make the "Why?" carry the correct emotional content. By describing the prior acts of the friend Lizzy, you create the emotional situation without explicitly stating the emotion. You could even leave out the word suspicion and let the physical response carry the feeling.
Gemma had heard this kind of suggestion from her friend Lizzy before, and the last time, her friend set her up on a blind date with Lizzy's cousin who had spent the whole time staring at Gemma's breasts. Gemma's shoulders tensed and her eyes tightened. Her voice dropped an octave, and Gemma loudly replied, "Why?"
You could also add italics to the word to magnify the effect (although it isn't very visible with such a short word). Bold makes the words loud if desired, as would CAPITALIZING.
Any sufficiently clear physical reaction to the suggestion would deliver the correct content like her stomach knotting, or the thought of a blind date sending a chill down her spine. A hard stare also shows an intensity of emotion.
You can also mix up the words a little to give suspicion. So "Why, exactly?" clearly shows suspicion and a desire for clarification. Stating someone's name without explanation is calling someone out on questionable behavior, so "Lizzy." expresses incredulity. "Lizzy!" takes it even further to express anger at an assumed transgression. "Lizzy?" expresses a lack of understanding, and delays Gemma needing to give a response, allowing her a moment to consider a response while forcing Lizzy to give a clarifying statement.