What is the etymology of the adjective "bumper"?

Looking at Etymonline and Dictionary.com only reveals that it was slang from 1759. Why did bumper come to mean unusually abundant, and why is it always paired up with the word crop?

The Oxford English Dictionary provides an enlightening quotation under the second meaning it gives, which is "anything unusually large or abundant." The quote is from 1759 and came from The Gentleman's Magazine:

In some of the midland counties, anything large is called a bumper, as a large apple or pear.

It then has quotes which uses bumper in various contexts, as for a large sum of money, a high score in a game, a very full brook, etc. Only one of these uses the now predominant form of "bumper crop".

The OED does not offer a definitive etymology, although it does suggest it may have come from the verb bump. It does seem plausible that in casual speech an unusually large object might have come to be called a "bumper" from the impact it might make when deposited onto a surface.

According to your Etymonline link, bumper in the 1670s referred to a "glass filled to the brim". Perhaps this definition of "fullness" expanded over time to include swellings in general, although I can't find a good reference for this. The term 'bumper crop' may then be used to refer to a harvest so large that it swells the bags or containers used to transport the crop to market. This seems to be one theory.

There is also a suggestion that the top edge of a silo is called a 'bumper', and thus a 'bumper crop' would fill a silo. This sounds a bit dubious to me, although the image of a full glass is congruous with the image of a silo filled to capacity.

As per the Word Detective. (If you're not familiar with him, do yourself a favour and lose yourself in the back issues.)

"Bumper" in this sense is just a superlative, meaning "unusually large or impressive." What makes "bumper crop" seem mysterious is that this "jumbo" sense of "bumper" is now very rare anywhere except in the phrase "bumper crop." But back in the 18th and 19th centuries, it was common to hear shopkeepers talk of "bumper business" in the holiday season or even "bumper traffic" on city streets. "Bumper" as a noun was even used as theatrical slang for a sold-out house at a performance.

The logic of this "large" sense of "bumper" is a little hazy, but a clue may be found in its earliest use. A "bumper" in the 17th century was a large glass of beer or wine that was filled to the brim, i.e., with the liquid literally bumping against the rim of the glass. Such abundance was obviously considered a good thing, as "bumper crops" of just about anything have been ever since.