As Barrie England's answer indicates, an entry for the phrases "yea big"/"yea high" appears in Wentworth & Flexner, Dictionary of American Slang (1960). But perhaps the most interesting part of that entry is the source note accompanying it:
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. A sophisticated fad phrase since c1955.
The expression "sophisticated fad phrase" is intriguing, but I have trouble squaring the notion that the phrase is "sophisticated" with its popularity among down-home folks like the people I grew up with in the U.S. southwest. Maybe the fact that (as Stuart & Flexner notes) the wording is usually accompanied by a size indication—using one or both hands, or a thumb and forefinger—marks it as sophisticated in the sense of involving multimedia presentation.
I don't know where the "yea" (or "yay") comes from; but a person using the phrase normally performs the hand-motion designation of size simultaneously with uttering the word "yea," so I always took "yea" to be a close equivalent to "so" (in "so big" or "so high"). The phrase has been around since at least 1951 (see the examples below), but it may not be much older than that. My reason for saying this is that Harold Wentworth (one-half of Wentworth & Flexner) saw his very detailed American Dialect Dictionary through to publication in 1944, and there is no sign of "yea" or "yay" in the relevant sense in that book; I doubt that Wentworth would have missed it if it had been present at a significant level in one or another variety of U.S. regional English.
The earliest occurrence of a related phrase in a Google Books search is from MacKinlay Kantor, Don't Touch Me (1951):
"The little one? About yay big? We went to their— their quarters. We tried. I mean I tried. But she was having twoubles."
The next-earliest is from Printers' Ink, volume 243 (1953):
You clear away a pile of proofs yea high, and squeeze into a chair oppressed by the weight of depth-interview studies, sales statistics and fudged-up manila paper. You stare, mesmerized by a compact, streamlined cabinet on wheels that flirts across the room at you.