You ask a good question - here’s my take:

Every endorsement (presumably) helps with one or more voting/influencing/financially supporting constituencies. Which endorsements ‘carry the most weight’ are to some degree dependent on the campaign and the candidate.

Barack Obama endorsing Alexi Giannoulias for State Treasurer was a big deal because it gave Alexi a state-level (if federal) powerhouse endorsement to counter Michael Madigan (and the state party’s) preference for State Treasurer. Would Bill Clinton endorsing Alexi have been a bigger deal? I’d guess not as big a deal, despite Bill Clinton being the last Democratic president - although it might have mattered a lot, at the time, for fundraising with big donors. Part of it is a credibility issue of sorts - who really would believe that Clinton knew much about a state-level treasurer’s race? Did other more local-level endorsements (subsections of the state) help Alexi? Probably they did by helping gather votes and offering exposure/bringing foot soldiers to a candidate running for an office few voters likely think much about one way or the other.

Is there a difference between local, state and national office as to what endorsements are likely to matter most? Probably. What about different candidates/election years? Probably they factor in too.

So I’ll answer by saying that I think context matters a lot with endorsements. Bill Foster being endorsed by a state-level officeholder (Alexi Giannoulias) as well as a local congressman (Phil Hare) helps cover a lot of bases.