Verity boost increases precision strike chance by 1% per boost level. Actually game directly adds enough precision to equipped weapon to provide required benefits (depending on total damage). For example, lets take Kamaitachi weapon with 215 attack, 75 attribute attack and 0 precision (290 total damage, 0% precision strike chance). Verity (Lv. 1) adds 2 precision, Verity (Lv. 2) adds 4 precision, Verity (Lv. 3) adds 6 precision etc. This roughly corresponds to the precision strike chance formula
Bonus precision from Verity is calculated based on the base weapon damage. Any attack boosts are applied after this, thereby reducing the effectiveness of the Verity.