'evenly-applied' is a compound of 'evenly' and 'applied'. 'evenly' originates from Old English, specifically the word 'efen', where 'efen' meant 'level' or 'equal'. 'applied' (from the verb 'apply') originates from Latin, specifically the word 'applicare', where the prefix 'ad-' (in assimilated form) meant 'to, toward' and the root 'plicare' meant 'to fold or join.'

'apply' entered English via Old French 'appliquer' from Latin 'applicare'; over time the verb shifted into Middle English and modern English as 'apply', and its past participle became 'applied'. 'evenly' developed from Old English 'efen' through Middle English into modern 'even/evenly'. The compound phrase 'evenly applied' is a straightforward modern English combination of these elements.

Originally Latin 'applicare' had the sense of 'attach, join, bring to' (a physical joining); over time English 'apply' broadened to include 'put to use, put on a surface, or enforce', and the compound 'evenly-applied' came to mean 'distributed or enforced in a uniform manner' in both physical and abstract senses.