Not sure, and inviting response ... but I don't think the "reduced split between Vls and Vapp" is down to differences in weight. I think it's down to differences in C of G. Quite often, it's most accurate when you fill the aeroplane up - but when you don't fill it up, that's when there are most likely to be discrepancies in C of G position compared to what's programmed. If it were down to discrepancies in weight, the error would be biggest when the aeroplane was fullest.