A dance partner at a senior center insists that her dance instructor says she should always keep pressure between her back and the leader's hand.

And this position seems to be supported by this statement in a Wikipedia article as follows: "The follower must constantly keep a little pressure against the hand"

My question is: How does the follower do this and still adhere to the weight connection so nicely illustrated in this web site, i.e. how does one lean back against the leaders hand and still push forward as the leader pushes forward?

While I can't pretend to be an expert in this regard I think I am beginning to understand the true nature of this connection. As the male partner in standard dances my right hand does make contact with my partner but there is little if any pressure. I believe my partner would argue that she does not lean back at all rather she is always balanced when in contact with my hips and it is not any pressure of my hand that keeps her in position. If we both maintain our frame the contact remains without need for her to lean or for me to squeeze.

Pressure isn't exactly the right word. An experienced follow will use her lats to "fill" your hand and maintain constant consistant contact. This isn't exactly weight or force or pressure but rather a state of being in connection with a partner.