It looks like this to me:
Where the second box is the variable width option. If it helps I expanded my path.
No stroke, no variable width profile for that stroke. It appears your selection has no stroke- which if this is the case you wouldn't have a width profile. Unless I'm misunderstanding this, you have to add a stroke.
In addition to Adams suggestion, that you have no settings applied to the selection, it could also be caused by the selected paths having different settings, therefore it won't show any settings except the ones that are the same for all selected paths.
But you can then choose a setting that will be applied to all selected paths and then the settings will appear - because all selected paths have the same settings.