Are Fakes Being Unwittingly Sold As Genuine Coins

Are you talking about an ebay auction or one from a true auction house like Heritage? With ebay anything goes, at least for listing an item. Unless someone reports the auction to ebay it will go through. If ebay does catch it they will take down the auction and probably suspend the seller.

If it is a place like Heritage then someone probably isn't doing their job. My guess is the way a fake would get through there is if the coin is in one of the really good counterfeit slabs that aren't easily detected.

Plenty of fakes being pushed around and then sellers claiming ignorance.

Oh yeah, without a doubt.

I was informed that one of the true tests of a coin is its weight. Is that true?

Lets put it this way, if the weight is wrong it is almost certainly fake, but if the weight is correct it may still be fake. Back in the 60's some counterfeiters making fake error coins used genuine US mint blank planchets

Only good for a coin in really high grades and even then, far from fool proof. Remember that any coin as it gets circulated gets wear and that means it is less in weight than original. Some coins get corrosion on them and that actually adds weight to the coin. Scratches, nicks, dents, wear all take their toll on a coins weight. And as most already know, many counterfeiters use actual materials so the weight is correct. They are doing that to sell, not use.
It's possible every one of your coins is fake.
Well may not allllllllll.

Genuine US Mint blanks planchets are fairly easy to get ahold of because they tend to slip out with the regular coinage. They can often be purchased from dealers in quantity for a relatively low price. Used to be that cent or nickel planchet for a dollar or two apiece. Less in bulk.

Contemporary counterfeits that were intended to circulate as money did use either short weight /fineness planchets or different alloys because the profit was coming from the difference in the cost of the metal and the face value of the coin. Collector counterfeits often used the correct alloys and weights because the profit was the difference betwee the value of the metal and the collectors premium for the coins rather than the face value. Use of the correct alloy and weight makes the detection of the fake more difficult and allows the counterfeiter to pass more of them before the fake is discovered. (This is why the Chinese are learning and are getting away from the off alloys and are moving to the proper alloys and weights. Especially on their better fakes.)

Another case occurred back in the late 50's early 60's when a LOT of fake US gold coins started coming out of the middle east. At the time US citizen could not own gold, but they could own US gold coins. Even the common US gold coins tended to sell at about twice the value of the gold in the coins. So the counterfeiters could use full gold weight and fineness and immediately pass them for close to a 100% profit. Sure they could have used a lower fineness but once again lowering the weight or fineness would make it easier to detect and reject the fakes. (In some cases they even uses higher weights and fineness. than standard) It was a case of "pigs get fed, hogs get slaughtered." which is really a mixed metaphor when used with Muslim countries.

You can bet your 1849 Double Eagle that they (fakes) are being sold unwittingly, both raw and slabbed.