Something is "yay" big

The expression is actually (or originally) "yea big" or "yea high" where yea essentially means this.

Wiktionary has an entry for yea:

Thus, so (now often accompanied by a hand gesture)

The pony was yea high.

Unfortunately, I haven't been able to find definitions for this word (with this sense) in any other dictionaries online.

Yay is most likely a corruption of yea.

The OED records it as ‘U.S. slang’ and suggests it is probably from yea, yea being ‘a word used to express affirmation or assent'.

The OED’s first recorded use is this from Wentworth and Flexner’s 1960 ‘Dictionary of American Slang’:

Yea big, yea high, 1. This big, or this high, accompanied with the spreading of the hands to indicate the size; very large, or high, overwhelmingly large or tall. 2. Not very big or high.