Gnome proficiencies are listed as light hammer, throwing hammers, and warhammers.
But the racial tree 'Gnomish weapon training' applies to light hammers, light maces, light picks, shortswords, shortbows, light Xbows, light repeating Xbows.
Surely Warhammers and throwing hammers should be on that list and shortbows, shortswords, Xbows, light repeaters, and maces should be removed from it. Consistency is needed with the introduction a new race, and taking a scattershot approach like this isn't going to help.
If light hammers, throwing hammers, and warhammers, are going to be the racial weapons that's what should be on Gnomish weapon training not a collection of other weapons that are not.
As for ranged weapons there is no reason the that Gnomes couldn't be given "throwing Hammer expertise", as Drow are given Shuriken expertise. It would be in-line with the flavor of the build without amplifying other classes unduly, and it would give a option to beef up thrower classes other than Shuriken chuckers which Severlin Has stated was a goal.