I'm sorry, you have not had a response yet, so I'll try and kick things off for you.
What pen do you have? is it the pen that came as standard for the tablet?
If the cursor changes shape when tilting the pen, then I guess the hardware must have that capability.
Can you show us a screen shot of the brush preset panel with Shape Dynamics selected, and the options bar visible. (Ignore my settings)
I do have the default pen, which on the Wacom store is called the "Previous Generation Pro Pen" here Previous Generation Pro Pen with Carrying Case.
Opacity in the Transfer tab is set to Pen Pressure. Also one more thing I didn't realize before, but the brush is changing with the pen tilt as if it were changing the roundness, so its squishing into an oval instead of getting larger or smaller. Since you asked about my pen, do you think it's because the pen is older and I should get a newer model?
Lets start with the basics. Select this brush preset.
If I use this brush with the brush vertical I get the thinner black strokes, and with tilt, the wider red. Does that work for you?
If I switch to a plain hard round and set size jitter to Pen Tilt I get this with the pen held vertically
And this with it tilted. Elliptical cursor and wider stroke.
I don't know what the sensitivity is with pen tilt, but I am certain it is way short of the 2000+ levels available with pen pressure. What's more the brush stroke is never going to be smaller than the cursor, so you can't make thin lines without setting a tiny brush size. The bottom line is that using Pen Tilt for brush size is not a great idea. In fact I don't use pen tilt for anything because it lacks feel and sensitivity, and you just dob't get the same degree of control.
Thanks for the screen shot, but we need to see the Options bar as well. If you have these two icons turned on and set size jitter to Pen Tilt, what will happen is that it will switch back to pen pressure by about the second brush stroke.