e.g. if I get Muscle Toner R1 for 8000, would the upgrade to R2 cost 8000 or 16000? I can't find a ruling in sr4a, and flavor-wise I can think of justifications for either case.

No.

Unknown for SR4 but if SR3 is a guide, yes. Main rule book if you have it in upgrading gear.

Cyberware, I would say yes because its acting like an upgrade, but Bioware no because it is far more intracite in nature and more complex.

Pretty certain it's GM fiat, although the rule for it from the Missions FAQ makes sense to me:

What Mr. Shed quoted is the official ruling.

Personally, I use that most of the time, but I decide on a case by case basis.

Example:
Runner A has Standard Grade Wired Reflexes 1 and wants to upgrade to Rating 2 (standard grade as well). I'd say he can do it and pay the price of Rating 2 - the price of Rating 1
Runner B has Standard Grade Enhanced Pheromones, Rating 1 and wants to upgrade to Alpha Grade Rating 2. I'd rule that he can sell back the original for 30% and has to pay the difference.
Runner C has Standard Grade Reflex Enhancers, Rating 1, wants to upgrade to Beta Grade Rating 3, see Runner B

Edit: Of course, cultured bioware or beta or higher can't be sold back, as it is custom tailored to the recipient and therefore not usable by anyone else

RAW, you can't increment anything. At least, some people (including me) took that position in the last thread about this. 'Upgrading' augmentations of any kind (cyber, bio, etc.) is actually removing and replacing, just like 'upgrading' your computer's graphics card or hard disks.

I'd argue with that, from a fluff perspective
IMHO, cybertech of the same grade could be upgraded easily (depending on type, of course). The Reaction Enhancers upgrade could mean installing additional macguffins e.g.
As for Bioware, I'm almost completely opposed. You don't just add a lump of meat to an organ and it works better.
Off the top of my head, maybe bone density treatment.
Oh, and I calculate the damage of an operation off of the final essence cost (before dividing it) of the 'ware, as well.

Caveat, though: That's just my personal way of handling it, to my knowledge not supported entirely by RAW, just extrapolated. Not even a houserule, just flavour, really.

Not talking about fluff, though. RAW, you always remove and replace. I agree that in-situ and/or incremental upgrades probably *should* be possible for certain things.

Mr. Shed and Yerameyahu are right by RAW (you can replace and sell the old for around 30% book cost [with the exception of beta+ and cultured bioware which are tailored specifically to you and can't be resold]), but as noted not everyone sees eye to eye on this so see what your GM says.

As A GM I agree with Mr. Smileys...Hardware can be upgraded, Bioware cant as in order to upgrade it would require rtermoving it from your body and growing it some more (Not Possible to my Knowledge)

If we're talking about 'makes sense to me (=you)', then it really depends on the specific cyberware. You certainly can't upgrade (=modify in situ) the Grade of anything, for example, but it's probably easy to swap out the sensors/firmware in a Taste Booster. In theory, upgrading Dermal Plating *could* be just adding more Dermal Plating, and Muscle Replacement might just be adding more artificial muscles. … or not, though.

I'm not sure anything available as an item in SR4 can be 'upgraded', except patching up programs. You replace old programs with new ones, you replace old Response chips, old Sensors, old Gas Vents, etc. Can anyone think of actual 'upgrades' in SR4 at all?

Initiation?

Ha! Of items. There are definitely upgrades for skills, attributes, Adept powers, etc.

I think we're getting caught up in the details of wording again. the meaning of incremental increase could be fluff add a bit or remove and replace. The game mechanic is still the same however.

As I said not sure on SR4 but missions is not BBB FAQ so, "go with what works for you." is still nil persp.

Well, the OP asked about incremental upgrade cost, meaning 'am I buying a Level 1-to-2 upgrade, or am I buying a new Level 2?' The RAW for basically everything, but especially 'ware, seems to be definitely the latter. So it does matter what the fluff says about it. Certainly you can use any house rule your group likes.

To build on that, even in hardware you cannot incrementally upgrade something. If you want Response 5 on a Novatech Airware it costs you 5,250 , not 4,000 (the cost of the commlink then the difference in cost of Response 3 and 5 chips).