First of all, spinning thick and consistent is quite difficult to do! If you want thick, consistent, and lofty, this is potentially one of the most technically challenging yarns to produce reliably as a single-ply yarn. If you take millspun commercial yarns which appear to be this, and deconstruct them carefully, you can often discover that they are in fact plied yarns, or in some cases, mildly felted pencil roving that hasn’t exactly been drafted and spun.
Paula Simmons’ book “Spinning for Softness and Speed” goes into a lot of detail about light, lofty yarns. I highly recommend it for anybody interested in spinning that sort of yarn. I understand you can order it directly from her here:
The easiest way to get a thick and consistent single ply yarn is to predraft to roughly the thickness that you want, and then simply add twist. However, this generally produces a fairly dense yarn without a ton of loft, and is rather slow going. The “right way,” so to speak, is to master woolen prep, make rolags with hand cards, and spin one-handed long draw… and this will still have some variability in thickness! There are many things in between these two ends of the spectrum. From commercial top, you can get a pretty good lofty single by spinning from the fold, quickly (as in drafting quickly and using a light takeup on your wheel and practically flinging the yarn at the orifice).
The most reliable way to get a consistent and predictable bulky yarn is to spin singles which are consistent, and ply them, using a fiber that tends to want to bulk up (Falkland wool comes to mind, and merino doesn’t do too badly and is easier to find). In general, not considering the question of finishing or washing your yarn and how the fiber behaves, a 2-ply isn’t quite 2x as thick as a single, and a 3-ply is a little more than 3x as thick — yep, the 3-ply structure actually behaves differently from the 2-ply structure, and adds more bulk. Were you to spin the fattest singles you can, and then ply them into a true 3-ply yarn (not navajo plied), you would see very surprising bulk from them, as well as wear properties superior to what you would get from a singles yarn.
You can also do a cabled yarn; the easiest way to describe that is to say that you spin singles, and ply 2 together; then you ply 2 of those plied yarns together again, in the direction in which you originally spun the yarn. You have a plied yarn within a plied yarn! Cabled yarns are very stable and even, almost no matter what you started out with; a thick-and-thin slubby single, plied 2-ply and then plied again cable, will be much more consistent than you’d think.
One easy way to spin a cabled yarn would be to use the center-pull ball method (or similar ply-from-both-ends technique such as the Andean plying bracelet). Ply once, then wind another center-pull ball, and ply that in turn from both ends.
Lastly, when spinning a thick yarn especially, prep matters — even more than it does when you’re spinning fine. When you spin fine, you do a lot more drafting and you can correct for a lot of things in the course of that; and you have more twist in the yarn as well. There are just more places that’ll be forgiving of problems in prep — when you’re spinning a thick and lofty yarn, your prep has to be spot on, or you’ll find unevenness happens very quickly and there’s virtually nothing you can do to correct it once it’s in there (or at least, it’s quite challenging by comparison to fixing such problems in finer yarn).
Personally, I like to work at being able to spin practically anything imaginable; but for practical reasons, extremely thick and lofty singles are not always as good a choice as a plied yarn of a similar thickness, though of course, it depends on your application. As a matter of my own opinion, I am not a huge fan of extremely dense thick yarns; I don’t like the hand or the drape of fabrics made from such yarns (though they have their places to be sure).