In other words, what does having a heavier (more cargo spaces used) ship do in terms of my route planning? It seems that it takes the same number of jumps to go to various places, regardless of how much I'm hauling. Does it only affect the amount of fuel per jump used?
It will reduce you maximum range, and increase the amount of fuel used. Do your planning when fully loaded, or use the handy slider to simulate a full hold.
Apologies if my assumption below is not the case and apologies if you already know all this but....
I assume that you use the economical routes as opposed to the fastest routes tick box when planning your routes... (under the navigation tab of the galaxy menu, about half way down).
Economical route planning picks a line of the shortest jumps to your destination, this uses less fuel but takes many more jumps so takes AGES.... Fastest route will get you there more quickly (i.e. in many fewer jumps) but uses more fuel.
Being full of cargo drops your maximum jump range, but not by enough to limit most of the economical routes - you will see it's effect a lot more on fastest routes.
Make sure you plan your route when you have your cargo on-board, or as Dommarraa suggests, use the slider to simulate a full load. if you plot a fastest route while empty, then fill up your cargo your jump range will drop below some of the jumps in the route you have calculated and this can be mildly annoying to fatal depending on the situation.
So basically (again, to be technical), it simply increases the fuel cost of individual jumps? Of course, more fuel spent per jump means (naturally) less distance can be travelled before refueling, but it isn't specifically/separately altering maximum range in addition to increasing fuel costs, right?
Dom specifically stated that it reduces jump range. Reduced fuel economy a side effect of that due to how fuel use is calculated. You can see the difference between laden and unladen jump range in the outfitting screen.
Most likely your ship can carry so little cargo or has so little jump range to begin with that the difference is not immediately apparent.
Perhaps two ships flying in tandam could carry a cargo of tropical palm nuts?An African or a European ship? (Sorry, couldn't help it.)