In boxing, mma, mauy Thai or any other martial art, when you're in your stance, does balance depend on equal weight distribution or what?
Martial arts and sports collectively have a huge variety of stances, some of which have weight equally distributed between the feet, while others have an unequal distribution, or even all the weight on one foot.
I answer here despite an existing answer because balance in boxing is managed very differently from arts like karate. In karate, the spine tends to stay more vertical, rarely leaning side to side.
Static balance simply requires that the body's centre of mass is over the foot or feet that are on the ground: basically anywhere above the shape you'd get by tracing around both your feet and drawing lines from left toes to right, and left heels to right. The body's centre of mass changes depending on your body position too: if you are standing up with your arms hanging beside you, it is somewhere around 10cm lower than your belly button, near the height of the top of the hip bones, but it varies a bit with gender, physique etc.. But, if you raise your arms the centre of mass moves up too. If you bend forward 90 degrees and let your arms dangle downwards, the centre of mass will be outside your body: 10 or 20cms in front of your belly button. This diagram illustates this: http://karatecoaching.com/wp-content/uploads/2013/10/centre-of-gravity.1.jpg
Often in martial arts, the aim is not to be as stable as possible, but to be able to move very quickly and with little telegraphing, and movement in certain directions is more important than others. For example, if you simply stand facing your opponent with your feet side by side in no special stance, the opponent can very easily push or pull you forwards or backwards, but if your feet at apart, they'll find it harder to knock you sideways.
A typical "fighting stance" in karate or boxing is more - but not completely - side on, having one foot in front and facing predominantly forwards, with the other behind and angled somewhat forwards, lets you push forwards and backwards more quickly, which is crucial in fighting for closing the distance to strike, often while driving the hips around to create power, and backing away when necessary. The balance in such a stance is closer to being over the back foot, but not all the way: having the centre of mass forwards of the back heel is crucial for allowing an extension of the back leg to drive the body forwards, rather than upwards.
There's a misunderstanding here about stances. Stances are not actually things that you stand in and distribute your weight. I hope that isn't how you're being taught. They are tools you use to achieve a goal.
A forward stance for example may put 60% -> 70% of your weight over your front leg, but that isn't the point of the stance. The purpose of the stance may be to lunge forwards, or drive forwards. Possibly to take out the legs of your opponent.
Back stance might be to pull back, pull the opponent off balance towards you, possibly provide a leg for them to fall over.
Put another way, all stances are going to have varying weight distributions, based on what they're used for.
There's a quote I always remember from a teacher to think of stances as "the burned out shell of movement". The important bit is the movement, not so much the stance.