I agree with Lloyd and Rusty's comments about the quality of time spent with your son being the top priority. Be sure to take plenty of shots of him and the two of you together.
My son and I (occasionally my wife as well) have done a lot of extended day-hikes in the National Parks as well as some some 2 and 3 day hikes. My son is old enough (14 now) to haul his share of the gear however.
Personally, I'm spoiled enough to always want my DLSR with me these days, even if it means extra weight. On one 2-day hike last summer, I just took my Canon S100 P&S. While I appreciated the lack of weight, the quality of the landscape pictures was definitely underwhelming. I ended up with dozen or so good pictures of my son in various locations and a few with both of us, but most of the pure landscape shorts were disappointing.
So, I've decided to stick with one of my DSLR's when hiking somewhere with great scenery going forward. Last summer/fall it was my 7D and EF-S 15-85mm. Now that I have a 6D and 50 1.4 (acquired in December/January) I'll be tempted to try that combination. Although, as the OP pointed out, there will be times when not having more flexibility in focal lengths will be limiting. If I owned a 40mm that would be very tempting as a light weight option as well, as others have suggested (with the same single focal length caveat).
Last November, I made the mistake of taking my 7D, 15-85mm, 35mm 1.4 and 70-200 2.8 II in a backpack on a long day hike with lots of elevation change in Big Bend N.P. I got some great shots from the 70-200, but it felt like it weighed 40 lbs by the time we got back to the trailhead!
Not sure why I brought the 35mm, I only used it a few times and its not a small lens either.