Alright, someone mentioned compiling a list of augments for each item piece by stone so that we could A) see what sort of augments are available for each piece and B) how certain stones weigh certain augments. I'll be keeping a list of them here in the OP with all listed augment combinations as data. I'm sure that augments are consistent between pieces of the same set, but as a just in case I've separated them anyway.
When rolling augments via a stone, you have three types of augments:
1) Attribute: STR, DEX, VIT, the like.
2) Parameter: Atk/Ratk/MAB and Acc/Racc/Macc. There are two rolls for this.
3) Utility: This varies widely based on the type of armor you're augmenting, as well as its path.
When you roll these augments, the type of stone you pick favors a higher value in their specific category. Taupe Stones favor the Attribute category, Pellucid Stones favor the Parameter category, and Fern Stones favor the Utility category, meaning that most of the time, you'll see higher values in the category your chosen stone favors.
However, augment exporting via Gearswap as well as some “bugged” augments have shown that after those three rolls, there is a chance of up to two additional rolls after for the Parameter category, which is often what leads to multiple higher values. Values of >30 on the Parameter stat are, as far as known, the result of two rolls of the same type being added together. We have yet to determine the rarity of these rolls.
Below is the list of various sets and weapons, as well as the paths available for each and the maximum range of each augment. Note that all forms of Attribute have been seen on multiple pieces, so this will not be listed, as any Attribute can pop up on any given piece. Only Parameter and Utility augments will be listed.