According to the Focal Dictionary on Photography the linear aspect of dilution depends upon HOW MUCH the developer has ALREADY been diluted. Roughly, it is like this:
If developer is very strong, a 2x dilution from that strength will NOT require doubling of development time. On the other hand, if you are starting with a VERY weak developer (say, Rodinal 1+99) and dilute THAT 2x, you will need perhaps MORE than a doubling of development time.
This kind of makes it easy to judge how dilute your developer really is: when a doubling of development time is required, then the original development strength was already moderately diluted. Maybe this is a good determinant for knowing how much to dilute, as the doubling will not give 'compensation' (yet), if 'only' a doubling of development time is required, but further dilution might start to do that.
Again, roughly, and from my 'un' scientific (but considerable) experience: take a developer like D-76. I would say that if you START with a dilution of 1+2, I would consider THAT to be a good benchmark. FROM THAT, if you then dilute THAT concentration 2x (i.e., now 1+5) you will now have to develop for twice the time. In other words, in dilutions that we traditionally consider normal (i.e., D-76 straight or 1+1) you will NOT have to develop for twice the development time, as those dilutions still hold the developer in the sufficiently 'strong' category. Of course, the extreme dilutions I speak about (1+5) will PROPERLY develop film (yes, they really will) but either you use LONG development times or you add a bit of sodium carbonate in order to speed things up.
Dilutions GREATER THAN 1+ 5 (with most normal film developers like D-76 types) start to offer real 'compensation', in that the highlights will not develop fully but the shadow detail will, even with continuous agitation. This sometimes leads to problems with negatives that will lack contrast because of this stricture. A practical limit for D-76 is 1+5. I know that this assertion is considered heresy (we are acculturated towards the status quo, folks; one never reads about this extent of dilution; thus it 'must' be incorrect, right?) but it WILL develop negatives well (and you do NOT have to use more than 250ml for a 36 exposure roll, either). Actually, Ilford allows dilution of its ID-11 to 1+3 but Kodak does NOT allow such with its D-76. One of these manufacturers is (yes, foolishly) incorrect with this, as these are the same developer. All I am saying is that you can go even one step further with the D-76 and dilute as high as 1+5. Excellent negatives, folks, but be prepared to either 'accelerate' or spend a lot of development time, or use higher temps (like I do, with, also, a bit of carbonate added, without any problems whatsoever). - David Lyga