It definitely goes back to the sixties, and it's definitely linked from the start to pesticides and chemical fertilizers (other early targets were additives to color fruits and veggies - oranges and carrots and so on, and the alimentary waxes and coatings) and also with the growing obsession of consummers with "flawless" and uniform products that made percentage of grown products rejected and thrown away at the source go sky high. Organic displaced as buzzword what was more frequently called "natural food" and "natural" growing methods at some point. For early discussions of organic food (and realize how similar their discourse about it is similar to today's concerns/beliefs), one just has to watch old interviews with hippies. In the 1990s, it simply started becoming mainstream.

There may be some confusion because a lot of people became aware of the "organic" phenomenon only when the debate on GMOs arose, and because there's a continuum and people into organic food were unsurprisingly among the first to worry about GMOs or to militate against them.

There's also a lot of cynicism toward organic food from people who became aware of the phenomenon only once the food industry caught up with it and saw "organic" as an added value they could use to justify higher prices, and started labelling anything and everything as organic and, following mostly lobbying from producers and customers that's when some standards (varying widely from country to country, some of those have governemental standards, others have certification from all kinds of organisms, farmer unions for instance) started to appear, to which the food industry replied by replacing mentions of organic growth by logos, to perpetuate the confusion with the new certification logos (and largely succeeeded).

For sure the original organic phenomenon wasn't about jacking up the prices. On the contrary, the early organic farmers were militant (many of those smaller scale farmers still are, and growing without pesticides has become one issues among many others like proximity to the buyers, GMO-free etc.) and doing all they could to bridge the price gap and become competitive to escape the small and elitist "health food" market, but had tons of problems with that challenge. They started getting a break when more people perceived organic growth as an added value, but as soon as that reached a critical mass, the food industry caught up and found ways to cash on it. That set back the small scale farmers again, though many also started to get creative around the same time, for example uniting as very large scale cooperatives to retain the proximity/organic methods philosophy but be big enough together to stand a chance to compete with the traditional food industry.

Personally, the first time I saw organic veggies/fruits in stores was in the mid-80s (that corresponds to the time I left home to study and started making groceries, however), though I've seen organically grown products not sold under that "label" much earlier than that at farmers markets.

Another thing to keep in mind is that for people of let's say my dad's generation (a few years too old, and much too conservative to be a hippy or listen to much they had to say!) "organic" growth methods were not a "new fad" for home gardening, but rather it's the wide use of pesticides and fertilizers that was a new and in his case short-lived fad - aping the "modern methods" developped for the large scale farming industry. For a few years in the 70s my dad used chemicals in the home garden before returning to the traditional methods his dad had used, and stick to heirloom seeds (for many years just out of annoyance of the sterility of the hybrids that forced him to buy seeds each year). For him it was far more having observed no significant advantage to using those pricey chemicals over the methods he had seen his dad use (composting, manure, bug nets, bug-repellent companion plants etc.). By the time he started passing his gardening knowledge to me, his methods were the same but his motives to use the "old ways" had evolved quite a bit.

As for the future of "organic", I guess the fad itself will eventually disappear from labelling and such. I know a great deal of farmers who've switched to "virtually organic" methods for all sort of motives (from constraints due to the banning of several chemicals to conviction or concerns etc.) and just don't bother with getting certified as organic producers as they see that as a costly gimmick in itself.

It won't disappear nearly as fast as some think, though, because the food industry has adapted to the phenomenon and found ways to use it. They have a long tradition of cashing in on "food frights" (there's an excellent discussion of this, mostly from the FDA/American angle and from the scientific perspective in Modernist Cuisine, interesting all the more because they don't find the organic phenomenon very convincing on many specifics from the scientific standpoint. It's mostly the FDA they lambast for "promoting pseudo-science" among the American public (and because the FDA is very influential abroad, worlwide) and having their hands virtually tied by the lobbies of the food industry, however.