Balance & Ichor: Based on what I can see, there's no statistical correlation to what determines balance (and by extension Ichor) - it's just purely a trait of the Blood Code you choose and just serves to further classify a given code to a 'role': Tanky fighters have the highest balance, Agile fighters have moderate balance, and casters have awful balance that's usually offset by high Ichor. Artemis can be thought of as the highest-balance caster type Blood Code (has 30 max Ichor), while Heimdall has the highest-balance of an dex/evasion-based class, but their values still pale in comparison to any of the heavyweight pure-fighter blood codes.

Weight Thresholds: I found these stats the most interesting, and useful for explaining exactly how equip load works. Equip Load has five different tiers represented by colored arrows (two down, one down, none, one up, and two up). From what I can figure, the thresholds at which you hit each of these tiers is percentage-based on your listed maximum equip load:

• Very Light: 0-20% equip load
  
• Light: 21-50% equip load
  
• Normal: 51%-100% equip load
  
• Heavy: 101-135% equip load
  
• Very Heavy: 136%+ equip load

Different blood codes each have their own base mobility ratings, which usually correspond to appropriately increased or decreased equip loads (i.e. the 'Slow' mobility blood codes often have very high equip loads, around 240+, whereas 'Quick' mobility codes have very low ones around 60.) The end result is that each blood code generally hits the sweet-spot of about 50-100 to have a 'Normal' mobility, but this does affect how the thresholds generally are centered around this.

• 'Quick' blood codes can get higher weights while retaining a quick movement speed than others, but they become 'Slow' rapidly after hitting that limit. Their Heavy equip-load range corresponds to normal mobility, while Very Heavy is Slow movement.
  
• 'Slow' blood codes retain Normal mobility at much higher equip loads than others (usually around 120-125) but they have a very hard time gaining Quick Mobility. Light equip load corresponds to normal movement, while Very Light is Quick movement.

There's columns in the table for determining the thresholds at which each code changes mobility classifications. Of note is that the Ranger has the highest possible weight (of classes that I've viewed) for retaining Quick mobility with up to 70, while Hades, Fionn, and Berserker enable Normal mobility at the heaviest possible equip loads of 125, without extra gift usage.
Isis is also a notable outlier for being a low-balance caster Code that has an equip-load profile consistent with the heaviest classes (slow with 249 equip load) which, while this makes highly-evasive quick casting difficult, does make it a great candidate for heavyweight caster veils such as Hedgehog Fort or White Vestment.
Last thing I'll say on equip load, the Queen's Breath Gift of Revenant's Ambition increases equip load by 30% of the given code's max. From what I've seen this benefits codes with already high equip loads to start with the most: This would make the heaviest possible 'normal' movement score 162.5 (extra 75 points of weight on Fionn/Hades/Berserker, halved due to weight threshold calculations) with this gift, and the heaviest 'quick' movement load 91 (21 extra points on Ranger).

HP & Stamina values: Initially these showed directly-measured values of the different blood codes ingame (without any extra gifts added in). Now they've been distilled down into something that (at some point) should be generalizable to different character levels hopefully.
The HP/Stamina are shown as abstract scale values - the higher the number, the more HP or Stamina the code has. Realistically, these are calculated by combinations of stats, with some extra factors of level, gifts, and also the hidden layers of scaling/math internal to the game for exactly how all these scale together to get your final HP/Stam values. Through some calculation I figured out how the values generally are sorted based on just the stats alone, as that was the easiest of the variables to manipulate (just by switching codes).
The way that HP and Stamina are calculated/graded are as follows:

• HP is most strongly correlated with high Vitality, with Strength contributing a quarter as much as Vitality does.
  
• Stamina is most strongly correlated with high Fortitude, with Mind contributing a quarter as much.

This can explain some phenomena seen in the table: Artemis and Mercury have the same amount of HP, where Artemis has a C+ in Vitality but a D in Strength. Mercury has only a C in Vitality (one rank lower), but makes up for it with its B Strength (four ranks higher than D), and the end result is identical HP values.
Because HP and Stamina change per level up, the previous values weren't exactly pertinent and some of those values might have been measured incorrectly. This is a first step towards creating a formula that might be able to figure out how the values are calculated in the long-run.
It should also be noted that adding passive gifts that manipulate the scaling stats do NOT boost HP or Stamina to any significant degree. Usually the modification is only by a single point - this is proportionally more useful for stamina, but in both cases is essentially negligible. Instead it's much more valuable to use the passive gifts that directly boost HP or Stamina. That all said, with an A+ in both Strength and Vitality, the Atlas blood code has more HP than the others by a landslide, And Ishtar has a lesser lead with its stamina, with the only A+ Fortitude being backed with an A mind stat.

Unique Gifts: These are also listed since, along with the stats, they can and should be treated as a potential selling point for a specific Blood Code once unmastered Gifts are taken out of the picture. Prometheus is notable for the only Blood Code to have more than one unique Gift, but it should be noted that the Eternal Blade Dance passive, unintuitively, only takes effect when the Blade Passive active is in use. (there's also Astraea, which is a season pass exclusive).
I also use a '&' character to denote gifts that are truly unique to the class. This is because some unique gifts can massively change how the game is played - Queenslayer's Final Journey provides massive stat bonuses with a tradeoff that encourages extreme aggression and finishing battles fast, for example. However, others such as Atlas' Firm Stand have later ability substitutes that achieve extremely similar effects (Warrior's Feral Tenacity) and are exchangeable. These substitutes aren't always 1-to-1 (i.e. Firm Stand is a passive, Feral Tenacity is active), but the distinction is that the truly unique gifts are a larger factor as to whether to select a given Blood Code or not.
Others such as Scathach's Peony Flash are just alternate attack types that have substitutes in other gifts (this might be a bit subjective however...) As a result, these unique gifts are prefaced with an '#', so when filtering they will appear below the '&' entries - These can be considerations for using a given Blood Code, but not as heavily as a mechanic-changing Active effect or Passive.

That should be all for now. Let me know if there's any issues or anything I missed!