Well, examples are better than words in my humble opinion. All below examples are using your code, with some additions.
The first example will prove that using shawn.prototype = new man; you're calling the constructor twice
function man(h, w) {
    SendMessage("man is created with height " + h + " and weight " + w);
    this.height = h;
    this.weight = w;
}
man.prototype.name = "man";
man.prototype.double = function() {
    this.height *= 2;
    this.weigth *= 2;
}
function shawn() {
    man.apply(this, arguments);
};
function SendMessage(msg) {
    document.getElementById("Console").innerHTML += msg + "<br />";
}
window.onload = function() {
    shawn.prototype = new man;
    
    var p = new shawn(180, 90);
    SendMessage("Shawn height: " + p.height);
}
<div id="Console"></div>
 
 
As you see, the constructor is called twice - once with no arguments then with the actual arguments you give it.
The second example just proves that using the subclassOf solve that "double calling" issue.
function man(h, w) {
    SendMessage("man is created with height " + h + " and weight " + w);
    this.height = h;
    this.weight = w;
}
man.prototype.name = "man";
man.prototype.double = function() {
    this.height *= 2;
    this.weigth *= 2;
}
function shawn() {
    man.apply(this, arguments);
};
function subclassOf(base) {
    _subclassOf.prototype= base.prototype;
    return new _subclassOf();
}
function _subclassOf() {};
function SendMessage(msg) {
    document.getElementById("Console").innerHTML += msg + "<br />";
}
window.onload = function() {
    shawn.prototype = subclassOf(man);
    
    var p = new shawn(180, 90);
    SendMessage("Shawn height: " + p.height);
}
<div id="Console"></div>
 
 
The third example shows what's wrong with your idea of shawn.prototype = man.prototype and I'll explain. shawn inherits from man so I've added new method that should affect only shawn, called marriage (that of course cause him to gain some weight ;)) - that method should not affect the base class man as it's not inheriting from shawn, inheritance is one way only. But.... as you see in the example, ordinary man can also get married - big problem.
function man(h, w) {
    SendMessage("man is created with height " + h + " and weight " + w);
    this.height = h;
    this.weight = w;
}
man.prototype.name = "man";
man.prototype.double = function() {
    this.height *= 2;
    this.weight *= 2;
}
function shawn() {
    man.apply(this, arguments);
};
function SendMessage(msg) {
    document.getElementById("Console").innerHTML += msg + "<br />";
}
window.onload = function() {
    shawn.prototype = man.prototype;
    
    var p = new shawn(180, 90);
    SendMessage("Shawn height: " + p.height);
    p.double();
    SendMessage("Shawn height: " + p.height);
    
    shawn.prototype.marriage = function() {
       SendMessage("Shawn is getting married, current weight: " + this.weight);
       this.weight += 20;
    };
    
    p.marriage();
    SendMessage("Shawn weight: " + p.weight);
    
    var q = new man(170, 60);
    q.marriage();
    SendMessage("q weight: " + q.weight);
}
<div id="Console"></div>
 
 
Finally, the fourth example shows that using the subclassOf everything work fine, as shawn inherits man properly, and marriage is not passed to the base class.
function man(h, w) {
    SendMessage("man is created with height " + h + " and weight " + w);
    this.height = h;
    this.weight = w;
}
man.prototype.name = "man";
man.prototype.double = function() {
    this.height *= 2;
    this.weight *= 2;
}
function shawn() {
    man.apply(this, arguments);
};
function subclassOf(base) {
    _subclassOf.prototype= base.prototype;
    return new _subclassOf();
}
function _subclassOf() {};
function SendMessage(msg) {
    document.getElementById("Console").innerHTML += msg + "<br />";
}
window.onload = function() {
    shawn.prototype = subclassOf(man);
    
    var p = new shawn(180, 90);
    SendMessage("Shawn height: " + p.height);
    p.double();
    SendMessage("Shawn height: " + p.height);
    
    shawn.prototype.marriage = function() {
       SendMessage("Shawn is getting married, current weight: " + this.weight);
       this.weight += 20;
    };
    
    p.marriage();
    SendMessage("Shawn weight: " + p.weight);
    
    var q = new man(170, 60);
    if (q.marriage)
        q.marriage();
    else
        SendMessage("marriage is undefined for man");
    SendMessage("q weight: " + q.weight);
}
<div id="Console"></div>
 
 
Hope this makes some sense! :)