There are those two similar projects:
Zepto.js
Zepto is a minimalist JavaScript library for modern browsers with a largely jQuery-compatible API
This is a somewhat old question, but I would like to add performance. From what I'd heard, Zepto performed better than jQuery.
This jsPerf shows different results. I can use jQuery's class selection (of a single element) 137% as often, compared to Zepto's. For ID selection, I can use jQuery's 285% as often.
That's a huge deal considering on most applications, DOM interactions are the only performance statistic that matters (other than network requests).
Also looking at that perf, I can see that I could do document.getElementsByClassNAme 8326% as often as jQuery, so we should all ditch all of these if possible :-)