ΔE 15.1, loose: different enough that you should pick on purpose. Weathered Skin is noticeably darker, cooler than Sickly Pink.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 15). Weathered Skin is noticeably darker, cooler than Sickly Pink.
The same difference applies the other way round: Sickly Pink is noticeably lighter, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Sickly Pink on the colour wheel See Weathered Skin on the colour wheel
All matches: Sickly Pink equivalents · Weathered Skin equivalents