I am confused. Does "Weber" fitting mean "AN" fitting? I would assume these both refer to the 37° flared tubing fitting.
Anyway, the barb-style "socketless" hoses are made by all the big guys now-- Aeroquip, Earl's, and Russell.
Braided stainless has big advantages in key areas-- they are almost indestructible, and they will never leak if properly assembled. It's a PERMANENT line. Think of it more as flexible hardline.
I think that Rob is giving good advice. The socketless, barb-style fittings don't care about the line, as long as it doesn't leak. Replacing the banjo bolts with these relieves a LOT of restriction. The socketless should give you the advantage of the AN style fittings while being cheaper than braided stainless.
BTW-- I went with braided stainless on my Fuel Press gauge install only because they don't make socketless in a -04 size. Smallest I saw was -06.
I would run -08 fuel lines. 1/2" ID line will supply all the fuel you will ever need.
HOHN