'branchlet' originates from English, specifically formed by combining 'branch' (from Old French 'branche') with the diminutive suffix '-let' (from Old French '-let', ultimately from Latin '-ellus'), where '-let' meant 'little'.

'branch' passed into Middle English from Old French 'branche'; the diminutive suffix '-let' was added in English (via Old French influence) to create 'branchlet' in modern English.

Initially it simply meant 'a little branch' (a diminutive of 'branch'), and over time it has retained that core meaning as a term for a small branch or twig.