A variety of things could be causing your problem.
Hard to tell without being there, but in your second photo, it appears that the fit of the driveshaft to the bearing may need to be checked.
But that could just be an optical illusion due to either the photography or my poor vision.
"Start from the ground up". Sorta like building a house, it all starts at the foundation.
We're not building precision machinery
per se, but minimizing tolerances at each step helps prevent the compound errors that may have us scratching our heads later on.
Here are a few ideas.
1. Check the shaft for straightness and roundness.
I was taught to use v-blocks and a dial indicator, but I'm not sure if that's needed for our purposes. Maybe, maybe not.
You mentioned that you rolled the shaft and visually compared it to another shaft. The visual comparison to another shaft doesn't really tell you anything other than one shaft appears as "straight" as the other- it doesn't prove they are both straight.
The rolling test is simple and reliable enough providing your test surface is as flat as the tolerances you need to hold. Rolling on the typical benchtop is where a lot of people think they are using a flat surface, only to be surprised when it is properly checked. If you want to use the benchtop as a flat surface to roll, it's best to use a good straightedge to check the surface for flatness.
A granite surface plate is a reliable surface for the roll test; a piece of plate glass is (usually) flat enough, too.
Or whatever surface you trust to be the flattest available to you.
With all that said, purposely-built shaft material is normally straight enough for our needs. But every manufacturer has boo-boos, and who knows what can happen between the time it leaves the manufacturer and finally gets to you.
At any rate, it's best to check the shaft for straightness. The shaft itself is the "foundation" of it all, and any other testing is pointless if the shaft is not already straight enough for your needs.
Another thing to watch for is a shaft that's out-of-round. Again, seldom will you have one that's bad enough to cause problems, but you never know. In particular, I've had some shafts with full-length keyways that were not as round as I would like.
The simple tests used to check straightness can also usually give enough of an indication concerning roundness.
2. Check for concentricity.
A more common problem with shafting is closely matching the shaft diameter to the bearing bore. This was mentioned above, and it is an area often overlooked.
The shaft itself may be straight and round, but it can be forced to rotate in an eccentric manner. In other words, the center of the shaft does not line up with the center of the bearing.
Due to the nature of our construction and the parts we're using, obtaining perfect concentricity is very rare. That's OK; it's not like we're building a CNC machine. But we should strive to minimize tolerances here, because loose tolerances translate into compounded errors later on.
Some types of bearings have opposing setscrews to help alleviate an improperly-fitting shaft. The idea is to move the screws on each side further in/out to help center the shaft in the bearing. I have no experience with these types, but the same concept is used in lathe chucks.
Personally, I would rather have a good fit to begin with.
A good way to check if this is an issue is to use a dial indicator to check for excessive runout of the shaft while it's mounted in the bearings. This is based on the premise that you have already checked the shaft itself for acceptable straightness and roundness.
If you don't have an indicator (even the cheapies will work for this), you could eyeball it like Rudy described. It's better than not checking at all.
Something else to consider is that, although rare, it's possible to obtain a defective bearing. I remember one time when I actually measured the shaft and the bearing bore. "According to the numbers" (yeah, right, we all know how that can go:les

it should have been a nearly perfect fit, and it was indeed tight. The problem was not the fit; it was the bearing itself.
But even after that experience, I still wouldn't jump to conclusions and suspect the bearing, especially if it was of reputable manufacture.
3. Mounting/alignment
I don't think mounting inaccuracies are causing your "wobbling" problem, but you never know...
Two types of alignment you're dealing with here: a). the alignment of the bearings to the shaft, and b). the alignment of the shaft to the rest of the machine.
a). I have been told that the type of bearings being used in this application are designed to accommodate
slight variances in angular alignment.
Naturally, you should try to keep the bearings as square to the shaft as possible, but if the shaft turns freely in the (mounted) bearings, you should be OK as far as alignment of the bearings to the shaft is concerned.
b). The alignment of the shaft to the rest of the machine is primarily done to ensure the grinding belt rides properly. If the shaft is squared to the frame, then you have a good baseline to align the other wheels in the system (tracking and idler wheels, etc.) to make everything coplaner.
But your problem is wobbling of the drive wheel itself, and I don't see where this type of misalignment would contribute to that.
4. Drive wheel
If steps 1 & 2 check out OK, the next thing to suspect is the drive wheel itself, especially if it has an unknown history.
Rudy hit the nail on the head concerning this.
Use the dial indicator to check the wheel the same way that you checked the driveshaft. (As always, make sure the indicator is firmly mounted.)
In the abscence of an indicator, a spacer block and set of feeler gages might work.
Many things can contribute to a "bad" wheel, but at least by this point you should be able to tell if it's the wheel or something else.
5. Sheave (pulley)
The pulley can be checked in the same manner. It's not at all uncommon to have it out-of-round, eccentric, or whatever.
But with the design of your mounting system, the chances of a "bad" pulley causing your drive wheel to wobble seem very slim.
The shaft is solidly mounted in the bearings, which are anchored to the frame.
The (pulley) belt is the "weak link" in the design to first absorb the stresses caused by an out-of-spec pulley.
The belt will wear, the groove in the pulley will wear, and the bearings will wear.
Excessively worn bearings could potentially translate into wobble on the other end, but you're having a wheel problem with fresh bearings right out of the gate; if the sheave were the culprit, it hasn't had a chance to affect your bearings yet.