The blob brush isn't drawing a "stroke" so you can't apply the stroke profiles as you would a stroke from the pen tool or whatever. What you end up with is a filled object with no stroke.
What might work for you would be to make a profile that's essentially there and back again twice - if you're looking to fatten the middle, make a stroke profile that goes from skinny to fat to skinny to fat to skinny... Does that make sense? Essentially, you'd be looking to go around the perimeter of the entire shape you've made with the blob brush. (Oh, and you'll have to add a stroke to the shape that you made with the blob tool to apply it to...) Shown here in grey on black to accent the change:
Hey Grant - are you talking about the Width Tool (which would be applied to the actual stroke) or the Distort>Bloat effect? I'm not familiar with the Bloat Tool, per se... OOOoooohh... Just found all the other options under the Width Tool... I don't use it much, so I often forget about it, but it's nice to know all those various tools are there. Thanks for the reminder. (They are all definitely the wrong tool for the job, but good to remember!) Thanks.
Yep, double-click the toolbar icon -OR- hit ENTER with tool already selected. And some tools queue up their properties dialogue if you simply click on the drawing board, like the Spiral Tool (which is nearly useless until you tweak it to your needs).
Aunt Illy is secretive, but she opens if your patient.