Learn English – the origin of “stat”

It comes via real-time strategy games, where one goal of the designers is to keep things balanced for all the various players; deviations from that goal are carefully scrutinized by the community that plays the game. More precisely, it comes from the regular complaint from certain types of gamers QQing over their losses — usually due to their inferior skill at the game — that the game's mechanics are broken or imbalanced.

Using imba, then, as a shortening of imbalanced, is a facetious way of mocking that attitude, by declaring even acknowledged essential parts of the game — such as the Hunter class in World of Warcraft, or some of its top players (usually insanely good ones) — imbalanced because in a way, if you don't know how to handle uber classes or uber players, they "break" the mechanics, albeit in a legal way.

In "Glossary of supposed Americanisms" by Alfred Langdon Elwyn (1859), I find this:

Let on, to mention. "He never let on," he never told me. An Icelandic word, laeta. (Brockett.) "He never let on to me about it," may be heard not unfrequently in the country.

The "Brockett" referred to appears to be "A Glossary of North Country Words", by John Trotter Brockett, FSA (1846) but I can't find the reference to "let on" or "laeta" in the samples that Google provides.

The first place I've found it used with the implication of "lying by omission", as in your example, is in a story called "Little Fairly" by Samuel Lover, Esq. R.H.A. in "The Dublin University magazine", Volume 1 (1833)

"Well there's the scales for you," says big Fairly, and away the little chap wint to weigh his goold (as he let on) as he did before.