you wrote: "Does this mean that the weight actually should be a little bit more on the heels?"
No, not in my experience. Actually, you open the Yongquan point by grasping a very little the ground with the toes. It will lift up a tiny bit the arch of the foot. Do it first with your intention only and then add a very light physical gesture. Nevertheless, the weight can be distributed quite equally all over the feet. Put down first the heels, then the exterior edge of the feet, then the toes -from little to big-, grasp lightly the ground with the toes (without tension), and find the center of your feet, and settle your weight there.
English is not my native language, so my explanations may not be as accurate as needed..
you wrote: "Is it the same thing as pushing a little bit forward from the shoulders? If I do this, I feel like there's more tension in the shoulders."
I am not sure I understand what you mean.
What I do is rounding a little bit the upper part of my back without compromising the verticalness of the posture: the shoulder blades move away a little from each other, and this gives the back some light stretch and opens the Dazhui. So yes, there is a little tension, but not pain or anything that could prevent you from resting in the posture and more importantly from breathing normally (normal abdominal breathing). What can happen after some time is that the arms feel like they are suspended in the air without effort from you.