What do these returns look like with a skilled butcher?  Does it matter?  Wiki says it is only speed that is affected, but one whack with a legendary butcher on a 25000000 size creature should show a difference if there is any.

Relative sizes of body organs may affect it too. So dwarves would net more liver if they were gigantic .

What's with the sudden jump in meat from 1900 to 2000 size?

From what testing I have done, the calculation of butchering yields seems to be broken down by body part.  Each animal's body is broken down into individual body parts during butchering.  The amount of meat/fat/bone/whatever on each part of the body is checked against some threshold, and if it exceeds that threshhold one or more units of meat are added to the tally.  At size 1900 a cow's upper body and lower body each add one unit of meat, but the other body parts are individually too small.  At 2000, the legs are each large enough to add a unit of meat as well, so the total meat jumps from 6 to 7.  Each leg is also large enough at that point to add one unit of bone.  There's a lot more than that going on - you always get one skull no matter what, and you get at most one skin, nervous tissue, cartilage, hair and tooth, and at most two eyes.

Based on Urist Da Vinci's excellent work above, and some testing of my own, I've worked out the basics of the algorithm that DF uses to calculate butchering results.

Dwarf Fortress starts by taking the size of the animal and from that determining the relative size of each body part.  In the body definition raws each body part has a RELSIZE number which determines how large it is in relation to the other body parts.  This is a relative number used to divide the total body size into per-bodypart sizes, not an absolute size.  DF seems to sum the total RELSIZE of every body part in a creature together, divides that into each body part's RELSIZE, then multiplies the resulting fraction

For example, in a cow the total RELSIZE of every body part is 9471.  The UPPERBODY part has a default RELSIZE of 1000.  Dividing that by the total gives a size fraction of about 0.1055.  In a size 600,000 cow, that body part has a size of 63351.

After determining the size of each body part, DF then checks each body part's size against a fixed threshold, which appears to be 185 (plus or minus five), from my testing.  If the body part's size is below this threshold, it yields nothing.  If the body part is above this size, DF adds one unit of product for every tissue type in that body part to the total.  The upper body of a cow is defined as containing hair, muscle, fat, and skin, so one unit of each of those is added to the total.  This is repeated for every body part in the animal.

Interestingly, DF does not seem to respect duplicated body parts of a single type during this.  Cows are defined in the raws as having twenty-four ribs:  seven true ribs on each side, three false ribs on each side, and two floating ribs on each side.  Butchering ignores the NUMBER tag in the bodypart definition and only treats cows as if they had six ribs, one of each type on each side.  This is also why you will only ever get at most one tooth from butchering a cow, no matter how large the cow is, despite the raws defining cows as having 30 teeth.

In very large animals, each body part may yield more than one unit of tissue.  This appears to be nonlinear - it doesn't start happening until you get to quite large creatures.  For a creature in the normal size range of a cow or most other domestic animals, each body part still gives at most one unit of meat/fat/bone/whatever.

Some tissue types - skin, hair, nervous tissue, cartilage - produce one object of variable size, rather than a stack of uniform-sized objects you get of meat and fat and bone.  If an animal has a skull, that is always produced as a result of butchering rather than being processed into a stack of bones.  Getting a skull happens no matter how small the animal is - so long as the animals is a slaughtered tame animal, anyway.  A butcher won't touch a wild animal corpse if all it would yield is a skull.

There's also some effect of variation of individual animal size, fat level, and meat level, on how much fat and meat you get back.  I am not at all certain how this effect works.

Small animals - rabbits, cavies, guinea fowl, ducks and buzzards - will never (or almost never) give anything on butchering because none of their individual body parts will ever be large enough to give one piece of meat.  Mid-sized animals give meat based not directly on their size, but on how many body parts they have which individually are over a certain size.  Only for very large animals is meat return directly proportional to size, and I'm not sure how linear that is yet.

Hmm, this is most interesting. I guess if somebody with the mathimatical know how were to run this against the body size ratios, they could figure out just how big something has to be to make it count.

   
These body modifiers give individual dwarves different characteristics.  In the case of HEIGHT, BROADNESS and LENGTH, the modifier is also a percentage change to the BODY_SIZE of the individual creature.  The seven numbers afterward give a distribution of ranges.  Each interval has an equal chance of occurring.

   [BODY_APPEARANCE_MODIFIER:HEIGHT:75:95:98:100:102:105:125]
      [APP_MOD_IMPORTANCE:500]
   [BODY_APPEARANCE_MODIFIER:BROADNESS:75:95:98:100:102:105:125]
      [APP_MOD_IMPORTANCE:500]

Since a cow has:

   [BODY_APPEARANCE_MODIFIER:LENGTH:90:95:98:100:102:105:110]
   [BODY_APPEARANCE_MODIFIER:HEIGHT:90:95:98:100:102:105:110]
   [BODY_APPEARANCE_MODIFIER:BROADNESS:90:95:98:100:102:105:110]

Statistics tells me that 68% of all cattle are between 0.90 and 1.10 times their base size, and that 95% of all cattle are between 0.80 and 1.20 times the base size. The maximum and minimum size multipliers are 0.73 and 1.33.

Its worth noting that the biggest possible rabbit or cavy is still too small to yield more than a skull.

Fat has the [THICKENS_ON_ENERGY_STORAGE] token, and muscle has the [THICKENS_ON_STRENGTH] token, but there is no info that I can find on how that all works. "...with great muscles and copious amounts of lard
" descriptions should mean more fat/meat, but how much more?

Check the string dump on the wiki.