Half ton towable, maybe. Depends on the truck. What usually gets people is neither the trailer dry weight/loaded weight/vehicle tow weight, it's truck payload.
For example, your trailer dry weight is 7,000 lbs, but loaded it'll will be heavier, perhaps 9000 lbs or so. For stability, most trailers put 10% to 13% of the weight on the tongue, so that 9000lbs translates to 900-1170 lbs tongue weight. Great, you say, your half-ton payload is 1600 lbs (varies from truck to truck, btw), so you are golden. Not so fast, bunkie, what do YOU weigh? Your wife? The kids? what about the generator and bikes you threw in the truck bed??? And don't forget about a full tank of go-juice at 7.4 lbs per gallon.
With only 700 lbs (or maybe only 530 lbs) left for all those people and fuel and stuff, you might easily be overweight on that payload. (Lessee, 225 for me, 145 for wife, 22 gallons at 163, two e-bikes at 55@ for a total of 643 lbs . . . .
For YOU, @Mtwolfer, your 3/4 ton truck is probably fine. Your brother-in-law's 1/2 ton, maybe not.