OEM crossbars are manufactured by Thule, AFAIK, so they should be good enough. Regarding carrying capacity, they are all made to be carried by any roof rack approved by local regulatory bodies (I would avoid Aliexpress racks for obvious reasons).

Size wise the most important part is the hatch clearance. Measure the box's rear overhang from the rear crossbar mounting position and compare it to the car's roof with the hatch open.

 

I also just noticed the max weight is 100lb for the racks alone, 165lb for the rails. My box weighs about 40lb and it's "capacity" is 165lb, so I guess it would make more sense to go with the rails.

Unfortunately, I'm sure that would also be much more expensive after rails plus some kind of aftermarket rack system.

 

According to this:
2007-2011 Honda CR-V Roof Rack 08L02-SWA-102 | OEM Parts Online
the roof racks load capacity is 75 pounds. How much does the Thule box weigh?

I mounted a Yakima roof basket on top of my racks. Later I realized the basket weighs about 40 pounds, so it didn't leave me much load capacity after that.
75 lbs of load capacity seems a conservative number though.

 

Rhino explains this.

 

Also, according to the user manua:

"The maximum load for your vehicle
is 850 lbs (385 kg) for U.S. vehicles,
and 395 kg for Canadian vehicles.
This figure includes the total weight
of all occupants, cargo, and
accessories, and the tongue load if
you are towing a trailer."

Five people weighting 170 lbs already reach the 850lbs limit.
My car has side step bars, trailing hitch, roof racks and roof basket. At least 100lbs?
So if I carry 4 passengers, I'm already close to the limit without even using the trunk.
If I dont' carry passengers, then I have all the cargo area available.
I didn't think about this when I bought the roof basket. I though it would be useful, but I rarely use it. I guess it only makes sense if I have to carry something dirty or wet that I don't want to bring inside.

 

Skis/snowboards and (camping) gear make the most sense.