The stem to handlebar junction on my bike is about 3.5in above the nose of the saddle, from there North Road Bars sweep upwards and then backwards but the actual grips are not horizontal but angled at about 20 degrees downwards from horizontal, so that the midpoint of the grip is the same 3.5in above the saddle. I sit pretty much upright -- see the parenthetical note below about not sitting bolt upright if you value your back.
I find reach more critical than height, remember your body bends as an arc, on my bikes bars vary from level to 4cm below, but the reach is identical on all three.
It also depends how long your arms are. The sweep of North Road Bars plus height of stem to handlebar junction plus the width of the bars (620mm) plus long arms help me sit nearly bolt upright (you must have at least a modest forward inclination or irregularities in the road will kill your back) despite the huge size and long virtual top tube of my bike.
All of this gives me enormous feel for the road, and fine control at speeds (unfortunately these days mostly downhill) where your normal narrow roadie bars will put you in hospital if you sneeze.
I haven't weighed the bike with me on it, but I doubt that in such an upright riding position, and with the backwards sweep of North Road Bars, more than a quarter or even a fifth of my weight is on the front wheel. I can't say I've ever felt the front wheel going light, but then it is a great big hefty rim, with great big thick spokes, and roundabout a kilogram of tyre and tube, plus the biggest, heaviest SON hub dynamo and even the Cyo lamp must weigh something. But neither does the front wheel come down first or awkwardly when the bike takes air over some bump, so the weight distribution isn't too unbalanced. I suspect that the weight distribution is helped by a long rear triangle and the fact that the motor is, literally, in the bottom bracket directly under me.
However, to the contrary, as far as I can tell moving the hefty battery from the downtube to the rack has not upset the handling one iota. Weird.
In automobiles, according to a book I wrote on the subject (yeah, I know, you're going senile if you have to look up formulae in your own book), the longer the wheelbase, the more it matters to have substantial load in the centre of the wheelbase to avoid barbell effects. On a bicycle, the weight is so much less and always more evenly distributed than in an empty automobile, so it isn't difficult to set up a bicycle to be sweet-handling under most load and load-distribution conditions. I like my bike to understeer on the limit, simply because the roads here are so rough that you're guaranteed at least once a day to meet a bump that will cause a nervous bike (short wheelbase with too steep geometry, stupid light in all components, narrow handlebars, tyres too narrow to give adequate friction with road, adverse weight distribution magnified by other factors listed) to plant its rider, but which my bike shrugs off with only a small twitch of the front wheel, nothing to start me worrying about the weight distribution.
A newbie might say, Hey, the question was about saddle height, so why are you talking weight distribution? This is why: Since the rider is usually, even under loaded touring conditions, the major weight on the bike, the height of the handlebars, which determines the angle of his back, is an important redistributor of weight. You can normally not adjust previously correct saddle height without deleterious effects on comfort unless you also change the handlebars. But, before a major tour or even a long ride, you can gain more advantageous weight distribution by fitting a different set of handlebars to move the bike's centre of gravity and its weight distribution by redistributing the rider. Check what a human head weighs...
