You select the line and then what do you do? You must actually draw the line
by dragging the mouse. Same with AutoShapes; you have to drag the mouse to
draw them. And the Line Weight button is not enabled unless you have an
AutoShape selected.
If you're dragging the mouse to draw a line or shape and something appears
to be created (has sizing handles) but disappears when you click away from
it, then this may be a result of your having reset the AutoShape defaults.
Users often do this to set No Line and No Fill for text boxes, not realizing
that text boxes are AutoShapes and that the defaults they set for them will
affect all other AutoShapes as well.