adverb
Non-standard variant of いっそのこと, used to express a preference for an alternative, often in a resigned or decisive tone. Less common than the standard form.
See also: いっそのこと
一層の事、諦めてしまおうか。
Maybe I should just give up.
一層の事、彼に任せたほうがいい。
It would be better to leave it to him.