I hope BDL will respond to answer your question.
Talking about this stuff it's important to be very clear about terms, because definitions are inconsistent. Different people use the same terms differently and with an equal claim to being right. As long as we're sure we're talking about the same thing, great.
"Thinning" is a term you see a lot on the knife enthusiast boards, but it's not one I like to use ordinarily, or at least without a lot of explanation, because it's ambiguous.
When I talk about "thinning," I usually mean one of three things:
- Some blades have a more obtuse face grind and/or edge angle at the heel than further forward (towards tip). Some sharpener/users feel they can improve the performance of the knife by making either or both more acute;
- When profiling a double-bevel* the sharpener creates a secondary bevel* between the cutting bevel and the face grind which is more acute than the cutting bevel on the way to profiling a double bevel;* and
- Re-profiling edge bevels with a coarse stone in order to return them to their desired angles after they've become increasingly obtuse with repeated sharpening. For freehand sharpeners, it's usually a good idea to do this every third or fourth sharpening. When I talk about re-profiling the original angle, or profiling an entirely new angle, I personally don't use the term "thinning;" but that's me.
*Note: The terms double bevel and secondary bevel can be ambiguous, too. Here, double bevel refers to a multi-bevel with two steps; while secondary bevel signifies the transitional bevel between the more acute face grind and more obtuse edge bevel.
The problem I had was that both sides of the edge are uneven, with one side of the edge ending up with a wider bevel.
The side with the narrowest bevel was the one sharpened with my left hand controlling the stone, so I feel fairly sure that what I did wrong has to do with my using more pressure with my right hand controlling than I did with my left. I also may have moved the stone faster with my right hand.
To even this out, can you just sharpen one side to even it out, or should I sharpen both sides, using more strokes on the narrow one?
You want your bevels widths even all the way along the length of the knife up to where the edge curves towards the tip. You also want to keep your bevel ratio constant at the desired bevel. If you have "low" spots on either side, you "section" the knife by giving those spots extra sharpening. At this stage of your sharpening career you want very definite, crisply defined, and straight bevel shoulders at the transition between knife face and edge bevel.
In order to see how well the shoulders are defined, as well as see the low spots as they develop, use the Magic Marker Trick. The Magic Marker Trick is one of the most valuable things any beginner can do to help himself.
If, after you learn to coordinate the movements it takes to use an EP, and after you learn the appropriate amount of pressure (as little as possible) it takes for efficient sharpening, you still find that one side sharpens more quickly than the other, then... Yes, you should consistently give the side which requires more time more time. This might seem obvious when you read it, but it's one of those things which requires either explanation or experience before it jumps out at you. In the meantime, the sides are probably sharpening at the same rate because you're using too much pressure on one side, and way too much pressure on the other.
Another Edge Pro question I have is when you guys sharpen a gyuto, how much overhang do you have from the table edge to the knife edge. Just seems like a lot, but maybe it doesn't make any difference.
Depends on the length and width of the knife. You should always have as much of the spine as possible against the table's stop. You'll have to rotate the knife a little to get to the tip, but that's okay.