'Respect' is Latin for 'look back at' — esteem grew from the idea that a second look means worth.
A feeling of admiration and deference toward someone or something; to hold in esteem or honour; in a particular aspect or regard.
From Latin 'respectus' (a looking back at, regard, consideration), from the past participle of 'respicere' (to look back at, to regard), composed of 're-' (back, again) and 'specere' (to look at). The PIE root is *speḱ- (to observe). The semantic development is illuminating: to 'look back at' someone implies giving them a second look — pausing to reconsider them rather than passing
The phrase 'with respect to' (meaning 'regarding') preserves the oldest English sense of 'respect' — not esteem, but 'a looking back at' a particular point. When a mathematician writes 'differentiate with respect to x,' the word 'respect' carries its original Latin meaning of 'regard' or 'reference,' not admiration.