If you use Inkscape 0.92.1 yes.
So, you've added a Spiro Path, which is in fact a path effect, with the "Triangle in" shape set - which also now includes a Power Stroke effect in the newest Inkscape.
Select your path with the Edit Path's by Node Tool. The very first node turns pink. This is actually the Power Stroke control.
If you click and drag that pink node it will thicken the line.
Example of Spiro stroke selected, showing path effects applied.
Example of clicking and dragging the Power Stroke control.
You don't even need to use the "triangle in" setting, if you have an ordinary stroked path, or a spiro path, you can add the Power Stroke effect. If you do that you get even more control with 3 Power Stroke controls which you can use to alter the thickness of the line. The top stroke below is a Spiro, the lower is an ordinary stroked path.
There's also similar functionality to the Pattern Along a Path effect, this time a circular control point controls thickness of the pattern.