Sodium sulfite is usually used as a preservative, accelerator and to some extent, solvent. Let's look at a simple developer, D-23, which contains only metol and sodium sulfite.(posted 8945 days ago)Metol alone isn't a very good developer; in fact, it does just about nothing before it dies from oxidation.
Add sodium sulfite, as in D-23, and it makes the metol "go to work," plus prevents the developer from oxidizing. At the sulfite concentration of 100g/L, as in D-23, it a) erodes/uncovers more development sites, which increases speed and, b) acts as a mild solvent, reducing filamentary development/clumping.
Developers are "complete."
That is, it isn't really necessary to add anything; most things you might add may give an advantage in one way while degrading the image in another way.
For example, Rodinal 1:50-1:100 is known as a high-acutance, grainy developer, but if you add a little sodium sulfite up to 50g/L, you can reduce the apparent graininess a bit...but you'll also reduce acutance a little too. It's up to you to decide whether or not the tradeoff is worthwhile.....or maybe use less sulfite?
Why?
Films developed in highly dilute Rodinal usually lose a bit of speed; for example, HP5+ in Rodinal 1:50 gives a "real" speed of about EI 200-250 or so. But add a little sodium sulfite, maybe 20g/L, and the EI climbs to 400, with virtually no visible effect on grain/acutance.
To go further, Delta 3200 in DD-X is _really grainy_, imho good for about only 8x enlargement tops. Add 50g/L sodium sulfite to the working solution and it takes a little of the edge off, yielding 11x prints that show finer grain the the 8x prints from negs developed without the sulfite. Of course they're not as sharp either, but they're sharp enough to be seen as sharp hanging on display.
One really shouldn't go adding sodium sulfite to everything willy-nilly, but you see that at least in some instances it can make a developer work better for its intended purpose.
Personally I think the idea of adding sodium sulfite to "expand the tonal range of the negatives" is ridiculous, a statement made by someone who hadn't the foggiest. My negs have a dead-straight "tonal range" of at least 15 stops, the limit of my testing, a far greater range than can be printed, and there's no way sodium sulfite could give them a wider range.
I suspect that idea came from the use of FG-7 with sodium sulfite; actually FG-7 is a good compensating developer which can compress the neg's density range so more of the subject's brightness range can be printed, but the sodium sulfite has nothing to do with that.
BTW, if you use a wash aid for film or fiber paper (and you really should), they're all solutions of water, sodium sulfite and often sodium bisulfite. So rather than buying the stuff as a liquid concentrate, just make your own by dissolving a tablespoon of sodium sulfite in a quart of water (more or less).