Melee weapon damage is partially dependent on weapon size, and increases as appropriate. Melee weapons being reduced in size is not going to be detailed here, since this is impractical beyond the Miniaturized modification (detailed in Equipment Modifications).
Flat +X Damage Weapons: These weapons do not increase in damage with weapon size, as the size is dependent on the size of their user.
1d4 Damage: 1d4 -> 1d6 -> 1d8 -> 2d6 -> 3d6 -> 4d6
1d6 Damage: 1d6 -> 1d8 -> 2d6 -> 3d6 -> 4d6
1d8 Damage: 1d8 -> 2d6 -> 3d6 -> 4d6
1d10 Damage: 1d10 -> 2d8 -> 3d8 -> 4d8
2d4 Damage: 2d4 -> 3d4 -> 4d4
2d6 Damage: 2d6 -> 3d6 -> 4d6
2d8 Damage: 2d8 -> 3d8 -> 4d8
2d10 Damage: 2d10 -> 3d10 -> 4d10