Upgrade your equipment, each one has a rating (ranging from D to A, with A being the best).
Good catch on weapon upgrading. For me, using the broken sword at lv0 does 226 dmg, while lv1 it does 229 dmg. Lv2 is now 233, so perhaps that is the "scaling" the tier provides or it's just an exponential scale based on the overall experience the weapon has. But I will say damage numbers do seem to have strange values.