most of the yarn alternatives the pattern lists (http://www.garnstudio.com/lang/en/pattern.php?id=4535&lang=en#tabs-3) are fine weight. they’re also in a variety of fibers, from cotton to merino to alpaca.
at joann’s you could try:
Deborah Norville Serenity Sock Yarn (merino/bamboo/nylon)
Deborah Norville Serenity Garden Yarn (dralon microfiber, but only self striping/ombres)
Purl Essence Pastel Party Yarn (antipill acrylic, and comes in white, grey, light neutrals, brown, not just girly pastels)
Premier Wool Free Sock Yarn (acrylic with PBT polyester, but only self-striping/ombres)
Patons Grace Yarn (mercerized cotton)
Loops & Threads® Woolike™ Yarn (superfine, acrylic/nylon, anti-pill)
also Patons Grace Yarn (mercerized cotton)
Loops & Threads® Snuggly Wuggly™ (acrylic, antipill, also comes in BIG! skeins)
and with that yarn weight, if you can find a sock yarn you like on sale, that’d work fine, you’d just need a lot of it.