More about BGP routing table
Weight is an attribute local to a router. The weight attribute is not advertised to neighboring routers. If the router learns about more than one route to the same destination, the route with the highest weight will be preferred.
The local preference attribute is used to prefer an exit point from the local autonomous system (AS). The local preference attribute is propagated throughout the local AS. If there are multiple exit points from the AS, the local preference attribute is used to select the exit point for a specific route.
Metric attribute is used as a suggestion to an external AS regarding the preferred route into the AS that is advertising the metric.