To avoid confusion we will refer to the "stars" as rank and the color of the equipment's name as the grade (when you hatch a Legendary pet a system announcement will say that you hatched a pet of Legendary rank).
There are seven possible grades of an equipment in AOT and can be determined by the color of the equipment's name (Regular, Good, Superior, Excellent, Perfect, Legendary, Divine). The grade determine the base stats that the equipment will have meaning the stats of the equipment before any enhancing.
There are other factors that will affect the said stats are the Equipment's Level (see level requirement) and the Enhancement Level (+8 on the picture). So if you want to increase the white stats simply enhance it or use Grade Enhancement on your equipment.
You can determine the rank of an equipment if you refer to it's stars. So far we've only seen an equipment of nine stars or Rank 9 (from a Game Master's equipment or from our equipment during the Prologue).
The rank will determine the base values of the blue options. The higher the rank the higher the value of the blue options. Besides the rank the other things that will affect the value of the blue options are the equipment's level, equipment class (Crusader, Mage, Berserker,Legionnaire) and sometimes if you are lucky enough you will have an equipment whose blue options value will be higher compared to an equipment of the same class, level, and rank.
There is only one way of increasing your equipment's rank and blue options and that is via Rank Enhancement.
Tips: Choosing the right options for you.
It doesn't mean that the grade or rank of a weapon is high that it is the ideal weapon for you, a common mistake of some people is choosing rank over the option. Some choose a 6-star equipment with crappy stats (for example an armor with Frost Def, Shadow Def, Crit Resistance, Physical Resistance) over a 5-star armor with good stats (Physical Def, Magical Def etc.). The reason for choosing Magical Def or Physical Def over the Elemental Defenses is that no matter the nature of the Elemental Attack (Frost, Fire, Shadow, etc.), you will still have a defense against it whether it's magical or physical.
For example if you battle a group of monsters having high Physical Frost Attack along with some monsters having high Magical Shadow Attack and all you have on your armor is mostly Frost Defense then you will be like paper to the monsters with the Shadow Attack. However if you have Magical and Physical Defense instead of just the Elemental Defenses you will be good on handling both attacks. This also applies when battling against other players.
You should also consider the blue options of your weapon. Generally the best options of a weapon is: Minimum Magic/Physical Attack, Maximum Magic/Physical Attack, Critical Percentage %, Critical Damage/Magical Damage/Physical Damage, coupled with your major Elemental Attack or the element of your Divine Skill or highest damaging attack.