It is currently not possible to adjust the size of pop ups in a web map. However, there is a project underway to rework pop-ups in ArcGIS Online that "should roll out sometime in 2018". Once these changes are applied in ArcGIS Online, they will also be migrated to Portal for ArcGIS in a future release.
FYI, please vote for this enhancement on the Ideas site,
Hope this helps,
So this was actually planned in 2018. As far as I know, it's still not rolled out.
Maybe in JS API v4 in the new Map Viewer and Experience builder?
I guess it'll never be rolled out for We bAppBuilder?