There is at least one significant difference in skiing "heavy".
There are a number of turn techniques that get used in different circumstances. Many consist of (in simple terms)
- unweight your skis
- turn your skis
- reweight your skis
I was taught that there are two ways to unweight you skis. One is to push down with your feet, effectively jumping slightly, making the turn before you come down from the jump. The other is to lift your feet, effectively just bring your feet up and letting your body "free fall" slightly, making the turn before your feet come back down to the ground. See erfink's comments for more details and videos.
I have always used the "jump" approach, and so do most people I know. But that becomes harder when you are carrying more weight. I expect that is why you are more tired. Hikers don't need to jump every ten seconds or so when doing a hike in their pack. Theoretically the "lift your feet" approach doesn't become harder. If you can make use of that I would try it.
You can also use carving turns where terrain permits. I fall naturally into carving turns on shallower slopes, and I expect that is why your tiredness is more pronounced on steeper slopes - you do carve turns on shallow slopes (which don't take much more energy in a pack) and switch to jump turns on more significant slopes. If you can carve more, that will reduce your fatigue.
In agreement with erfink who says "ski dirty", you might consider a more skiddy turn when terrain doesn't permit carving - maybe, as erfink suggests, a Stem-Christie. Consider using the pole more to do a controlled unweighting without the jump. Slower speeds will also mean you don't have to execute the turn as fast, which means the jump doesn't have to be as hard. It's the jump that will get you.