That varies with the bike. You need tools to fit all the fasteners needed to adjust brakes and shifters. Also to fit seat and seat post and stem. A spoke wrench is a good idea. A chain tool is a good idea. A Unior Cassette Cracker and a few spokes may be a good idea on longer tours. You need a patch kit, tire levers, and a spare tube. Most of that can be part of a small multi tool. The whole lot including the seat wedge should probably be less than a pound.

Rather than carry cone wrenches or heavy headset tools I rely on borrowing them if necessary. If you start out with well packed bearings there is little risk in this even on a coast to coast tour.

Will you need to remove pedals to fly home or to ship the bike? If so, whatever tool you need for that should come along unless you will be able to buy or borrow it at your destination.