The reason we can't apply a different stroke width to many stock icons such as the ones in the question is that they are not made of strokes but filled objects instead. This can be visualized by switching to path mode in Inkscape:
In the icon objects neither stroke nor fill is defined, making them more versatile for web customization.
To make the stroke wider we therefore first need to define a stroke and a stroke color in Object > Fill and Stroke properties. After that we can increase stroke width in the Stroke style tab.
To widen a stroke in a single object of the icon we may break apart the path Shift+Ctrl+K to then select the resulting sub-object:
After adding a stroke color black, and increasing the stroke width we will obtain a thicker arrow in above example:
Note that this will not change the object's geometry but the stroke thickness is added in addition.
To change an object's color we may define a fill, and the desired fill color similarly: