I'm a baritone, and when I started voice lessons, my breath support was better when I started paying attention to it in other contexts than simply singing. When I would walk, I would practice breathing and releasing the diaphragm (the organ located above the stomach), filling up with air and using that in my everyday breathing. Eventually, that method became my default way to breath.
I think the pressure to make big sound causes us to throat-sing much too often. You have to train the breath before it can work for you, and that can take weeks, even months (dare I say, years) of consistent attention.
