Coaxing them onto a truck scale in the wilds of Alaska isn’t practical. Besides, who’s going to push, pull, or shove a bear onto a scale?
I suppose one way is to throw the bear into a swimming pool, then calculate how much water it displaces. A bear will displace a weight of water equal to its body weight. At least, that’s how it works for weighing ships.
The standard method used by biologists is to shoot them with a tranquilizer gun from a helicopter. It’s not real clear exactly how they weigh a tranquilized bear. I suppose if they tried lifting a bear with the helicopter, and the helicopter crashed, they could write in their field notes the bear weighs more than the helicopter can lift. In any case, biologists don’t weigh bears all that often.
At least, not until now. Sometimes people get ideas. Like using sonar to find submarines, or radar to spot incoming bombers. A couple guys doing spatial work on buildings in Katmai National Park and Preserve near Brooks Falls, a famous bear-watching area, hit on the idea of using a laser scanner (photo) to measure the bears’ body volume. Then, by estimating relative proportions of body fat, muscle, and water, they used software to get an approximate but fairly close body weight. More volume, more weight. Read story here.
Might work on fat feral rabbits, too.