'appreciatorily' ultimately derives from Latin via the verb 'appretiare' (Late Latin), itself formed from 'ad-' + 'pretium' where 'ad-' meant 'to' and 'pretium' meant 'price' or 'value'.

'appretiare' passed into Old French as 'apprécier' and then into Middle English as 'appreciate'. From the verb 'appreciate' came adjectives such as 'appreciatory' and the adverb was formed by adding the suffix '-ly', yielding 'appreciatorily'.

Originally related to setting a price or valuing (literal 'price-setting'), the sense shifted to valuing, recognizing worth, or being grateful; the adverb now means 'in a manner showing appreciation'.