'properly managed' is formed in modern English by combining the adverb 'properly' (from 'proper' + suffix '-ly') and the past participle 'managed' (from the verb 'manage'). 'proper' originates from Latin 'proprius' meaning 'one's own, special', and the suffix '-ly' forms adverbs. 'manage' ultimately comes from Italian 'maneggiare' meaning 'to handle', from Latin 'manus' meaning 'hand'.

'manage' passed from Italian 'maneggiare' into Old French as 'manegier'/'manier' and then into Middle English as 'managen' before becoming modern English 'manage'. 'proper' came into English via Old French from Latin 'proprius'. The collocation of an adverb + past participle (e.g. 'properly managed') developed as a common English construction to describe the state resulting from an action.

Originally, 'manage' often implied physical handling ('to handle with the hand'), but over time its meaning broadened to 'direct, control, or administer'. 'Properly' retained the sense 'in a suitable or correct manner'; combined, the phrase now commonly means 'under correct administration or control'.