The word 'incrementally-grown' is formed from 'incrementally' (from 'increment') and 'grown' (past participle of 'grow'). 'Increment' comes from Latin 'incrementum', meaning 'an increase', and 'grow' comes from Old English 'grōwan', meaning 'to grow'.

'Increment' entered English from Latin via Old French, and 'grow' has been in English since Old English times. The compound 'incrementally-grown' is a modern formation, combining the adverb 'incrementally' with the past participle 'grown'.

Initially, 'increment' meant 'an increase', and 'grow' meant 'to become larger'. The compound now describes something that has increased or developed in small steps.