We're working on methods to prevent users from ripping off his work and republishing it, or more so from reproducing it offline, be it on mugs, or similar.
Sadly people either don't know, or don't care that it is illegal to steal someone's work and try to use it on mugs, shirts, etc, and try to sell it, as if it was their own...
One easy step to checking if someone is using your images is
You can easily do a Google image search to see if someone is trying to use the work in such a way as to make a profit on your work.
By Google Image searching you will find any related images to the one you have posted, and if someone is trying to make money off of your designs, you should be able to find it, but sometimes Google Image search isn't perfect, but it does a great job.
As for "how to stop someone from selling your designs" there is a really simple method, besides technical stuff...
That is sell Mugs, shirts, etc YOURSELF.
This way, if someone does try to rip off the work, there is no way that they will be able to make money, because you are the "Official Store" and who is going to want to risk a 3rd party, instead of the artist's store?
Now, as for technical aspects, towards comments such as "republishing" his work, there are a few steps you can use to at least make it harder for people to steal his work.
resize/lower-quality of the images
Link images from another site, which I believe will not have it as a loaded resource, but I could be wrong.
Disable print-screen. I am not sure how to do this, but I have seen it happen before, but there might be ways around that, but still makes it harder for users.
Detect action of print screen, right click and trying to save the image, etc, and call a command that would either overlay something over the image to block screen shots, or replace image to stop saving the image(have not tried this, so not sure how doable it is, but think it could work). You might also be able to detect and block the inspector, or be able to alter the source, but again not too sure.... I'm going to try this stuff out myself as well, so it's just theory for now.
Embedding special meta-data information into the Image that provides author information and copyright jazz. I don't know about this in detail, but have heard about companies doing it... This will only help if someone tries to sell the image online, offline wont help you.
You also can implement other things such as disabling right clicking, and even if some of these things can be bypassed, the question is "are they smart enough to bypass it?"
Some security is better than none
Overall, there are a bunch of different options to at least make it harder for someone to not only steal the images, but try to make a profit.
I say if you make a store yourself, you will eliminate the biggest threat that seems apparent, and that is people trying to make money off of your designs. People only want to make money, so if that avenue is impossible, since you are already doing it, then they would probably try their time somewhere else.
Coupled with added protection against stealing the images, potential thieves will most likely look elsewhere, as they don't want to waste time, on something that isn't going to be profitable.