I found that the story of underwater pyramids actually predates the Weekly World News article. Its origins begin with Dr. Ray Brown, a "naturopathic practitioner" from Mesa, Arizona, who claims to have discovered a submerged pyramid in the 1960's/1970's while looking for sunken galleons near the Bahamas.
Dr. Brown claims to have retrieved a crystal sphere from within the pyramid that exhibits "mysterious powers".
His account, along with some video of the crystal sphere, were featured in an episode of In Search Of.... The relevant clip is available on Youtube.com.
The details of Brown's account seem to vary somewhat from telling to telling, but his claims of entering the pyramid (which appears to range from 80 feet to 400 feet in height, depending upon which version of Brown's story is told), finding two golden hands which he could not move, retrieving the crystal sphere from within those hands, hiding the sphere from his fellow treasure hunters, and the loss of most of his photographic equipment due to a storm (which is used to explain why there is no photographic evidence of his dive) are generally consistent.
A rather decent skeptical analysis of Dr. Brown's story and the mysterious crystal sphere (which is apparently in the possession of Arthur Fanning in Sedona, Arizona) can be found here. The author of this article, Dr. Gregory Little, a "psychologist turned explorer and documentary maker" devoted to investigating archaeological ruins that might be linked to Atlantis, provides this conclusion:
While I tend to lean toward the hoax explanation, the truth is that no one will probably ever disprove Brown’s story and it’ll be used time and again to support various ideas. I also confess that while the story seems very far-fetched, it’s also possibly true. The crystal does exist and many people swear that it has some sort of mystical power. As with all incredible reports, all of us can and will believe whatever we are predisposed to believe. I’m happy with ending by saying that I don’t think it’s true but I don’t really know. I’ll never know for certain and I’m okay with that. And with 5 divers supposedly seeing a mass of marble ruins spread across a vast area of sea floor I have to wonder why none of them went back or at least left some sort of written account of it.
He also related his correspondences with a man claiming to have been a long-time friend of Brown, who stated that Brown confided in him that the whole thing was a hoax:
After being a guest on the George Noory (Coast-to-Coast) show over a year ago I received an email from an elderly man who said he had been a friend of Brown since childhood. After exchanging a few emails he related that Brown confided to him that the entire affair was a hoax Brown concocted to take advantage of all of the media controversy that had been stirred up by the 1968 discovery of the Bimini Road. He explained that Brown simply wanted to be a part of it.
The More Recent Story
Regarding the more recent claim of verification of the "crystal pyramids", there seems to be no actual evidence supporting the claims available. It does seem likely that they are merely fabrications built upon the earlier story by Dr. Brown.
The original WWN story1 cites only "Oceanographer Dr. Verlag Meyer". Other versions of this story exist, including one that claims "American and French" research teams found the pyramids in 2012 (this video actually references the WWN story that predates it by 20 years).
No other identification is offered in any of the versions I found, and I could find no reference to either oceanographer "Dr. Verlag Meyer" or the French and American research teams. The name "Dr. Verlag Meyer" itself seems rather strange, as I found a couple of people speculating that it was fictitious due to "Verlag" apparently meaning "publisher" in German.
One enterprising skeptic raised some good technical questions in the comments of this version of the story, inviting anyone to provide answers in a thread he dedicated to the topic in a SCUBA forum.
In particular, he points out:
The original ‘Ray Brown’ stories of the 1970s are false. There is no part of that area that a 1970s scuba diver could reach that we couldn’t find. He couldn’t go below a hundred feet for more that a couple of minutes with the equipment described in the story. Also, treasure salvors have no problem scouring an area that is shallow enough for sport scuba gear. There would be no hiding giant glass pyramids.
The current stories of French and American divers finding something in the Bermuda triangle are equally false and no one has been able to cite who these divers are. Because the exact location is never documented, we don’t even know if the depths involved can be dove without submarines.
When you look at the search and recovery technology of today, we could find these things. Read the stories of finding the Titanic or the treasure wreck S.S. Central America.
We have been unable to document the quotes from experts in these stories and cannot even document the existence of the named experts.
While he does not cite references or proof, I must admit that his arguments seem more likely than the equally unfounded claims of multiple, conflicting variations of these mysterious discoveries.
Snopes.com has recently addressed this story, as well. They have labeled this "false", citing similar rationale (primarily that there's no evidence to support the research, or even the identities of the personnel supposedly involved in the teams).
- Link taken from Oliver_C's answer