Being under 80,000 lbs gross isn't enough: the weight also has to be spread across the axles. A standard five-axle truck has three axle groups: the steer axle at the front of the tractor, the drive tandem (two axles) under the back of the tractor, and the trailer tandem at the rear of the trailer.
US federal limits on the Interstate are 20,000 lbs on a single axle and 34,000 lbs on a tandem (two axles more than 40 and no more than 96 inches apart). A steer axle is usually held to about 12,000 lbs by its tires and axle rating, and some states set a steer limit of their own. That's where 80,000 comes from: 12,000 + 34,000 + 34,000.
Groups of axles are also limited by the federal bridge formula, which protects bridges by asking for more distance between axles as the weight goes up: W = 500 × (LN ÷ (N − 1) + 12N + 36), where W is the most the group may carry in pounds, L is the distance in feet between its outer axles and N is the number of axles. A standard five-axle truck needs its first and last axles 51 feet apart to carry the full 80,000 lbs. A special rule lets two tandems carry 34,000 lbs each if they're at least 36 feet apart, first axle to last.
Where the freight sits decides which axles carry it. Think of the trailer as a plank resting on the kingpin (over the tractor's drives) at the front and on the trailer tandem at the back. A load near the nose rests mostly on the kingpin, so it loads the drives; a load near the doors rests mostly on the trailer tandem. A short, heavy load piled at one end overloads that end, even if the gross is legal. Spread it out, or center it between the kingpin and the tandem.
Kingpin at 0 ft, trailer tandem at 40 ft
20,000 lbs centered 10 ft behind the kingpin
On the tandem 20,000 x 10 / 40 = 5,000 lbs
On the kingpin 20,000 - 5,000 = 15,000 lbs
Two adjustments move weight without unloading. Sliding the trailer tandem forward puts more weight on the trailer axles and less on the drives; sliding it back does the opposite. Each hole on the slider moves a few hundred pounds, depending on the trailer and load. Sliding the tractor's fifth wheel forward puts more weight on the steer axle; back puts more on the drives. Many states limit how far the trailer axles may sit from the kingpin (California allows 40 feet for most 53-foot trailers), so the tandem can't always go all the way back.
The only way to know is to weigh. Drivers cross a certified truck scale after loading; the ticket shows each axle group. If the drives are at 35,200 and the trailer tandem at 31,000, the fix is to slide the tandem forward a hole or two and weigh again, not to hope the weigh station is closed.
Practice
What's the US federal limit on a tandem axle group, in pounds?
More info
Quick reference
Steer axle
Front tractor axle; about 12,000 lbs in practice.
Drive tandem
The tractor's rear pair; carries the kingpin weight.