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The bones hold the body weight in position more than the other way around.
The specific issue is keeping the bones of the feet in the desired alignment to support the body mass, against the substantially off-axis distorting force that is the weight of that body mass.
Standing barefoot, rise until your heels are about an inch off the floor and the ball of foot has risen slightly, so that only the toe pads (your most forward point of support possible) have floor pressure. The task of keeping the bones in your feet in position for this is what I am referring to.
In dancing you may generally prefer to use the ball of foot, however being able to support the weight two inches further forward means two things: If you go to the end of the toes just before leaving the foot, thats two inches less you need to reach you moving leg ahead of your body into your partner's space. Second, if you are carrying weight on the ball of foot and you start to accidentally overbalance forward, the ability to support your weight from two inches further forward than you were can help you recover.
Sorry, but that's simple not true. You can have all sorts of body alignment problems and still carry your weight forward on the foot - shoulders hunched forward being a commonly seen one.
What is true is that posture alignment problems can often be caused by an inability to supprt the weight forward in the feet. The common fault of leaving the hips behind in a forward movement is often little more than attempt to keep the balance back over the strong part of the foot, rather than bring it forward onto the weaker toes and then beyond, committing to the movement.
What is also true is that in a dance context, the inability to support the weight forward in the feet can often be caused by posture alignment problems. The common problem of leaving the hips behind in a forward movement is also often caused by some level of instinctual resistance to commiting to a forward movement when someone is standing directly in front of you, and may have nothing to do with inadequacies in the feet. The same people who might show this problem while dancing with a partner usually have no inadequacies committing their hips forward while walking.
That "instinct" to which you refer is their gut level awareness that their feet aren't yet strong enough to send their weight forward with the kind of control and support that would be polite to the person in front of them. Quite often they've even been scolded by teachers for making the attempt.