Hello Carlo
When configuring attributes such as weight (or any attributes in BGP), you must keep in mind that they affect the choice of route based on the same routing protocol. A router will consider iBGP and eBGP as two separate routing protocols. For example, if you have two routes to 8.8.8.8 via iBGP, then the weight can be used to force the router to route via one path and not the other. If you have one route via iBGP and the other via eBGP, the weight will not affect the choice. It’s like trying to make the router choose a path via iBGP and not via EIGRP by using the weight attribute. It won’t work.
What the router does use, before any of these attributes, is the Administrative Distance. Since it views eBGP and iBGP as two different routing protocols, the router will always choose to use eBGP over iBGP because it’s AD is 20 as opposed to 200.
I hope this has been helpful!
Laz