Byzantine weights are common and come in many shapes and designs. Here are a few.
The denominations are based on the weight of the gold solidus (nomisma) or the Byzantine ounce with 12 ounces to a pound.
Many solidus weights are marked "N" for "numisma" which means simply "gold coin." The gold solidus was precisely maintained at 4.45 grams for hundreds of years and I do not know why so many solidus weights weigh so little, often close to 4.3 grams or less.
The Roman pound was c. 324 grams and the weight of the pound declined gradually over time. It was 320 grams or less in Byzantine times.
A Byzantine weight marked "one ounce". The X-like symbol is for ounce and "A" is "one" in Greek.
26.92 grams. This weight has a squat barrel shape, 14 mm high and 18 mm wide.
(26.92 x 12 = 323 grams/pound.)
Bendall, Byzantine Weights, 33 (26.40 grams = 316.8 grams/pound).
A Byzantine weight marked "N" for "nomisma" for "one solidus".
4.29 grams. 15 x 14 mm.
This weight, and many other similar weights, is too light. Some schlars have said these were the minimum acceptable weights for a solidus. Personally, I doubt this. I think the value of 0.1 grams or 0.2 grams of missing gold was too much to overlook. (As I write, the modern value of 0.2 grams of gold is slightly more than $20.)
Bendall, Byzantine Weights, 103, 104 (4.11 and 3.84 grams).
I solicit explanations from readers. 
A Byzantine weight marked "N IB" for "12 nomismata".
54.17 grams. (4.51 grams/nomisma)
38 mm wide by 7 mm maximum thickness (the rim is above the field)
This seems to be a bit heavy with an weight per solidus slightly above the usual weight of a solidus.
Bendall, Byzantine Weights, 1134-5 (52.65 and 51.83 grams. Those would be 4.39 and 4.32 grams/nomisma).
A Byzantine two-ounce weight.
53.17 grams. (319.0 grams/pound and 26.59 grams/ounce)
28 mm square and 7 mm thick.
Γ B either side of a long cross.
The "Γ" is a Byzantine symbol for "ounce" and "B" is "2".
Bendall, Byzantine Weights, 71-73 (only #73 has its weight given: 52.50 grams (315 grams/pound and 26.25 grams/ounce).
The gouges across the reverse may have been intended to lower the mass of the weight. The weight have been too heavy when made and adjusted downward.