Hiking Recommendation

Yes, of course, you can add more weight to your backpack. It will indeed increase the Calories burn, since the Garmin watch measures the Calories burn from your heart rate (using also the HR Variablity, and the average Resting HR as reference), hence the increased effort for carrying the additional weight will result in higher HR, and thus in higher Calories burn.

But how does that relate to the exercise load?   For comparison, I run 4 miles on level ground in about 35 minutes for a load of roughly 200-240.   When I do a 4 mile hike with 2800ft vertical over 4+ hours, I get a load of roughly half that.  It seems like the hiking gets a bad rap when it comes to training load through the app.   

Hard to tell without making a lab calorimetry, but as I wrote the Calories burn is calculated from the HR. One of important factors that can infuence the results is the average Resting HR (RHR) for given day. So for example if the avg RHR is high on the day you do your hike, and low on the day you do the run, the run activity will have higher readings. Another factor is the HRV (heart-rate varibality) that is used to detect the anaerobic threshold and training stress, and may hence also influence the values.

Another possible reason is that you burn too much energy during your run, because of wrong technique, while you are quite energy efficient when hiking.