The largest I know of and remember was the Bigger Dawg launched by a couple friends in NC. It made the cover of one of the Magazines and weighed in at 562 lbs, I think. 24" diameter, but not real long as it was an upscale.
Motors, schmotors! Who needs motors anyway? Well I guess I do. But I won't need it until 10,000 feet or so... and then I am looking for a big push, a 75mm or 98mm.
Here's a qucik answer for a pretty good idea on what a motor will lift:
Take the average thrust and divide by 4.45. That'll tell you the average pounds of thrust the motor delivers. Then divide that by 5 to get the 5:1 safety margin that seems to be considered the standard in rocketry. I think you can fudge a bit on the 5:1 depending on the rocket and the wind but shoot for the 5:1 as a minimum.
For example:
An AT M1315 motor:
1315/4.45 = 295.5 lbs. of thrust average. Divide that by 5 = 59.1. So, a 59 lb rocket (loaded with motor) has a 5:1 ratio for that motor.
Or, the easiest to figure a Pro54 K445 = 445/4.45 = 100/5 = 20 lb loaded rocket for a safe liftoff.
This is a good starting point, especially on neutral a burn motor. However, it may be better to take a look at the actual thrust curve to see the initial thrust of the motor.
The easiest way to estimate the lifting power of a motor, or the minimum size motor needed to lift an airframe, is to divide the average thrust in Newtons by 25 or multiply the weight of the rocket in pounds by 25.
So an M1939 will be able to safely lift an airframe weighing :
1939 / 25 = 77.6 pounds
Or to safely fly a 100 pound rocket you would need a motor(s):
100 * 25 = 2500 Newtons averge thrust
So the 100 pound rocket reference earlier will need at least a M2400 motor or two or more motors with a total average thrust of 2500 Newtons or greater.
The above is not an exact method of calculating weight and thrust proportions, but it is an easy method of doing a "reality check" on motor selection. I use it when I'm RSOing to make sure that the motor selected by the flyer has enough thrust to get his rocket off the pad safely.
I never said it was getting off the ground using a rocket motor... only at 10,000 feet or so. It should already be travelling 70 mph or so when the rocket motor fires.
It was 102 meters tall, 10.06 meters in diameter, weighed 3,038,500 kg, and was a 3 stage cluster model. The first stage burned five W class motors rated at 6,747,580 newtons each. It cost $431 million to launch, in 1967 dollars.
Since HPR wasn't well standardized at the time, the engines were incorrectly labeled as F-1's.