I'm hiking the PCT(Pacific Crest Trail) this year with an olympus had some of the same concerns except I can get out about once a week. I am just going to carry extra batteries, but I fly radio controlled aircraft also, and there are plenty of somewhat light weight 12 volt chargers for lithium batteries, most cameras use a 2 cell lithium rechargable, but lighter still would be a car charger since it has one output voltage setting and fairly low input requirements in most cases.
Get any generic flexible solar charger that will recharge nimh or nicads probably will do 4 at once due to voltage constraints. I'm assuming your not going solo as I am so if 3 in your group carried a solar charger on top of their pack you wil have 12 charged cells to provide 14.4 volts. Most of the light weight chargers only charge AA cells but you can easily solder your own packs of cells. you will need to experiment to see if this is sufficient at low temps(note: specialty cells for rc motors can be discharged rapidly). Except car batteries are really more like 13 volts so you may need a resistor for cheap and dirty or a voltage regulator to connect to the car charger, I would probably test with 12 cells and see if the voltage and temperature are still reasonable before trying to regulate voltage.
I could easily make something like this work with a few hundred dollars in parts. I believe the weight to power ratio would probably not be worth it unless you could set up a large flexible panel in the sun during the day and hike only in the evening through early morning ie. night hike. But it would need to be tested in cold weather. The solar panels should be fine, except for power out put needed for your requirements. If your hiking how do you make sure your panel is receiving optimum sunlight? Will you be able to set the panels in the sun for the better part of the day? Instead of AA you may need sub C or larger so a larger panel but the batteries voltage/amperage testing would take time. Also you would have to determine how many days in a row you may have no sun? (weather related). How many Batteries per day will you need to recharge? How large a safety margin you want vs weight you would want to carry? possibly might be lighter to just carry a bunch of spare batteries.
Heres a company that makes what your looking for but in no way would the backpack actually work for a 3 week trek and from the reviews I've seen it is kinda short on power, And you still need the car charger.http://www.voltaicsystems.com/
I remember seeing an article a few years ago about a backpack design that creates energy from the up and down movement of the pack, I cant find it now and don't believe it was ever produced commercialy. Theres also someone playing with a knee brace generator.
I know you probably want a solution but I dont believe its praticable at this time. My base weight clothes, sleeping bag, back pack, stove, etc is under 13 lbs. Add food, water, camera gear im up to as much as 35 to 40 lbs. for 6 to 7 day sections Ounces matter to me and spare batteries make more sense. Sounds like a fun adventure have a great trip.