I asked a Brazilian contact what voz grossa means and what voz fina means. If he gives me permission to reveal his identity, I will give him credit in a follow up post, since I will no longer be able to edit this one.
He said that grossa means strong. And fina means soft.
When talking about voices we use the following vocabulary:
His voice is:
loud, deep, booming, a voice that carries, a voice that commands respect
Her voice is:
soft, weak, hushed, timid
He speaks in a deep voice and is easily heard.
She speaks in a soft voice and is difficult to hear. I wish she would speak up more so I could hear her.
Voices can be raspy, clear, menacing, comforting, gentle, sweet, whining, petulant (literary usage).