The scaling depends on how much lift you generate, the lift is a question of speed and your the available lift surface the nominal lift produced is then divided by surface area to give you your wing loading.
Solar is pretty much the most inefficient way of powering virtually any aircraft because you needlessly increase the weight of the lifting surface and batteries weight considerably more than fuel and that weight is dead weight during the entire flight while a fueled aircraft becomes lighter.
That said the scaling between the volume and the "surface area" isn't even in question here because you are going to be hitting a wall much quicker and that's takeoff weight as mentioned before lift is a factor of the surface area that can provide lift and the speed of the aircraft (as well as air density and some other things but lets ignore it) the heavier the aircraft the more energy you need to actually get to takeoff speeds, and when you make your lift surface bigger you increase drag as well as weight.
The speed you can reach is going to be more or less limited because even a 100% efficiency solar powered engines are going to be limited to the max cell efficiency * cell surface area, the 2nd part of the equation is your wing surface and eventually there is a limit to how big your wings can be and still support themselves and most importantly not flutter. When you take all that and more into account there is absolutely no fucking way that you'll make an aircraft capable of lifting a 50,000lbs of crago, heck you won't build a solar aircraft capable of lifting 50,000 lbs of anything including itself. To put that into perspective 50,000lbs is 1/6th of the maximum structural load that a 747-8F (freighter) can carry, and about 1/4th of the nominal cargo load.
To put it into even more perspective Solar Impulse weights 3000 lbs, it's maximum takeoff weight is about 4000 lbs and it has a max speed of 80km/h with a wing span greater than that of a 747. To put it simply there is no freaking way to scale this up, there is a good reason why nature haven't developed heavy flyers the heaviest bird capable of flight weights 35 lbs, the rule of thumb is that when you double the weight you need a 4th time as much wing area and spend 4 times more calories to achieve flight and while mechanical flight isn't exactly the same it's not that different - the amount of energy you can produce more or less limits how well you can fly because at the end if you stick 2 SRB's to a cargo container you don't even need wings.
P.S. And that's before we getting into finding a material light enough to be viable for solar flight while still being able to bare the load of 50,000 lbs without collapsing, but even if you'll take perfect carbon nano tubes or any other super material you still won't be getting off the ground.
If you want solar cargo air transport blimps are probably the way to go...
The issue with overly large wings is mechanical stress let's try and get around that.
<This is a dumb design> As a thought experiment, take 3 Solar impulse aircraft fly them next to each other with a simple non weight baring cable to share power between them. The outer two can clearly provide more power than they need and supply that extra power to the center one. Now the center one has extra power for 'free'. So, it can have a higher angle of attack and more weight.
As to scaling birds, a Quetzalcoatlus had a wing span of 9 to 12 meters. That's huge for a land animal. https://en.wikipedia.org/wiki/Quetzalcoatlus Birds are limited by biology not so much aerodynamic issues.
And again you are missing the point Solar Impulse can lift about 1000 lbs of w/e if you want to scale it up either increase the thrust by 50 or increase your lift surface by 50 to get to that 50,000 lbs cargo you want. If we ignore load baring and drag than 3 Solar Impulse aircraft combined could lift 3000 lbs that's it.
We can argue about this till the sun doesn't shine it won't change the fact that solar flight will never be a viable option for cargo transport. But it can replace other things, things that for example are well in range of the 1000 or lbs of payload that any reasonable designed solar aircraft could carry - surveillance, communications, weather and atmospheric monitoring equipment etc. They could potentially replace satellites, and increase the endurance of both military and civilian drones considerably but no one is looking at them to carry cargo because it's simply silly.
Also if you want to move 50,000 lbs today by air it usually won't take less than 6 days, the only thing you can really ship overnight are small things that end up going on commercial flights not cargo flights. And while it's also true that a container ship can take 21-30 days from say China to the US about 14-15 of those days are spent in local transit and loading, the sailing it self a cargo ship can do within 10 days of good weather with the average being probably closer to 12 or so days due to weather and fuel economy.
As a final point on energy larger birds can do generally have a slower metabolism. They simply need less energy per lb to maintain flight and can travel longer distances on smaller per pound energy budgets.
Not that I think anything could convince you, but look into glide ratios and optimum glide speeds. If A and B have 15:1 ratios and B glides at 2x the speed that's more efficient.
Amount of thrust (limited by solar power) * lift surface limited by materials and physics, it all boils down to math. http://www.ajdesigner.com/phpwinglift/wing_lift_equation_for...
So I really don't see any way of a solar power aircraft which uses aerodynamic lift getting of the ground even in the most perfect unattainable conditions.
Second wing area and lift is related to velocity (not power) right before you stall outside of that it's a looser connection. Velocity is indirectly related to power in steady level flight based on drag. Drag in level flight is a function of weight, shape, altitude, and velocity.
Economicly I don't think this is a good idea. Physically it seems possible with cheaper and more efficemt solar cells it might make this more reasonable up to a point. Especially if they can boost altitude and thus speed.
50x the power takes 50x the surface area and 7.1x the length / width. Or less than that with a lifting body approach. Or significantly less than that if it's daytime only.
Solar Impulse is a marvel of engineering, and the fact that during on of the legs of the flight a single person flew the damn thing for 6 days straight is an attestment to human ingenuity and courage but there is a very very big difference between flying 50 people using electric aircraft (again electric not specifically solar) in 50 years to flying 50,000 of lbs on solar power.
We already have electric aircraft capable of 1.5-2h of flight scaling those up on electric power alone without solar might actually be easier as you do not inherit the weight of the solar panels. Efficient fuel cells and ultra light batteries / nano super caps could potentially make electric flight possible within 50 years but again relying on solar to transport cargo long haul no sorry not happening.
You would probably want a thicker coating to protect the cell, but in 50 years solar can add very minimal weight.
Anything that will be dependent on aerodynamic lift alone literally won't be getting of the ground with any significant payload.