The first time I noticed it was in Apple's ad campaign:
Friend: I love the new Apple ad campaign. So elegant, so simple.
Me: [eyeroll] Yeah, except it makes them look illiterate.
Friend: How can it look illiterate when they're using photos of Mark Twain and Bob Dylan?
Me: Think differently. It's think differently.
Friend: Well maybe they didn't want to use an adverb. Adverbs are weak forms.
Me: It's still an adverb. Leaving out the suffix doesn't transform it into a non-adverb. The only word it could possibly be modifying in that two-word sentence is "think", which is unambiguously a verb. "Different" can't be a direct object or a subject, because it's not being used as a noun. Writing the sentence in natural order as "Different think" doesn't make any sense.
Friend: Oh whatever, but the sense is clear, and that's all that matters, right?
Me: Okay, so you're defending a company that's made its name on its design aesthetic and famously rigid attention to detail when they approve an ad campaign that gets the grammar wrong in a two-word sentence?
Friend: If Microsoft did the same thing you'd be defending them.
Me: Ah, no, because a) I don't use Microsoft products and b) I support choice in hardware and software...
If you know anything about the history of personal computing, you know we stopped talking about grammar then.
I don't know if it was the influence of the ad campaign, or if the ads were just illuminating that part of the zeitgeist, but it seemed that ever after that people were dropping "-ly" suffixes in print and speech. A neighbour a few doors down from me put a bumper sticker on his car that said, "Save the adverb". A lot of people who claimed to otherwise care about grammar and usage were claiming that the "-ly" suffix was going the way of "thee" and "yclept". They said it was "retrograde" to cling to it.
Let the record show: these people also tended to be the ones in my acquaintance who were completely okay with constructions like (dis)ease and inter/cut. Right.
That was then. Now telling writers not to use adverbs is considered standard advice — any adverbs, not just ones shorn of the suffix which tells the reader it's an adverb. Stephen King famously advises against them in On Writing, and other voices weigh in with their own examples.
The only legitimate reason I've found to chop out adverbs (general concerns about being too wordy notwithstanding) is that they are sometimes used to modify verbs which are too weak to show the action properly. Replace the verb with a more appropriate word, and the adverb is superfluous.
Example: He walked slowly down the street.
Change to: "He strolled -" or "He shuffled -" or "He dragged himself-" and get rid of "slowly".
Fair enough. However, I'd say in these cases it was never the adverb which was the problem, but the verb. The adverb swooped in and helped identify the problem, and got handed the blame for it. That's not a nice way to treat parts of speech.
To get rid of adverbs entirely is to get rid of an entire part of speech. Not a trope, or a convention, or a standard, but an entire chunk of natural language.
You may think differently, but to me that's reactionary and counter-productive.