The increase/decrease should respect the same precision displayed for line width in the layer properties (one decimal place).
When you look at the properties of a line, they display with one decimal (0.5, 1.1, 2.5, etc).
However, when you press the Up or Down arrow to increase/decrease the line width it rounds to a whole number.
Line width is set to 1.5
Click down arrow, it goes to 0
Why not 1.4?
To make it even more confusing, if you are at 1.5 and click up, it goes to 2.