The specs for most loaders and/or buckets will typically quote the bucket volume in terms of cubic yards. A typical CUT sized loader might have a 1/4 to 1/2 yard bucket or 0.25 to 0.5 cu-yds. It might also be expressed in cu-ft or cu-meteres, or liters, or some other measure of volume.
Sometimes two numbers are quoted - heaped and struck. Struck being if the material was level with the edges of the bucket (held open end up) as if a straightedge was pulled across, striking off the excess.
Heaped, while more closely matching real world use, is less precise because various materials "heap" at different angles. Water won't heap up at all while big chunks of sticky clay might hold an 80 degree slope without falling out of the bucket.
Convert the volume to cubic-feet.
Then multiply by the weight per cu-foot of the material in the bucket.
Some weights of common materials in lbs per cubic foot:
Aluminum, solid: 165
Brick, Red: 120 (packed solid)
Brick, Fire: 150 (packed solid)
Caliche: 90
Cement, Poortland: 95
Cement, Mortar: 135
Cedar, Red: 24
Clay, Dry, Excavated: 68
Clay, Wet Excavated: 114
Concrete: 150
Eartt, loam, dry, excavated: 78
Earth, moist, excavated: 90
Earth, wet, excavated: 100
Earth, dense: 125
Fir, Douglas: 33
Garbage: 30
Granite, solid: 163
Granite, broken: 103
Gravel, loose, dry: 95
Gravel, with sand, natural: 120
Gravel 1/4 to 2, dry: 95
Gravel, 1/4 to 2, wet: 125
Gypsum, broken: 113
Hay, pressed: 24
Ice, solid: 57
Ice, crushed: 37
Iron, solid: 450-486
Lead, solid: 708-711
Limestone, broken: 97
Manure: 25
Mortar, wet: 150
Mud, packed: 119
Mud, flowing: 108
Oak: 44-59
Sand, dry, loose 100
Sand, wet: 130
Snow, fresh: 10
Snow, compacted: 30
Turf: 25
Water: 63
