I've tried renaming and renumbering the connector ID's. Still, Apex orders the connectors however it wants. Seems to be tied to an internal number that isn't obvious or accessible to me.
It's odd now though that, in the attached image, the first connector I created was "Spot Weld (1)". It is no longer first in the list and renaming it or renumbering its ID doesn't change its placement in the tree sort order.
The order of the items is purely determined by the order of creation. However if you delete something and then undo the deletion, then that item drops to the bottom of the list. Might that be what happened with your spot weld?
You can click on the Name column heading to order things alphabetically. This is a global sort of everything in the browser, though: