it’s too fine for the logo I’m working on - the hairlines disappear when the logo is small

There are several faces with a range of size-specific fonts to address this issue; e.g. ITC Bodoni (3 sizes) or H&FJ Didot (7 sizes!).
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Prillwitz by Ingo Preuss is another – fresh – Didone. It has 3 different designs, one optimized for use on newsprint, one for text sizes and one for display sizes.