Here is an altered coin of Decentius from Lyon. Not surprisingly, since Magnentius and Decentius lost, the bust and name is mostly erased; but the Chi-Rho was not touched. The mintmark is also missing, but it is either RIC VIII Lyons 171, 173, or 175. This coin weighs 4.3 grams and it must have been made for use as a solidus weight. A solidus ideally weighs about 4.5 grams; but a little less was acceptable. However, some are a little more underweight because of clipping; which is why people made weights, to make sure that the gold coins were in the tolerable weight range. These weights occasionally turn up for sale, you can find more information if you search for exagium. These modified coins are often described as game pieces or tokens, but when they weigh a specific amount they must have been used as weights.

'Emperor Julian Augustus to Mamertinus, Praetorian Prefect. The purchase and sale of solidi are impeded if the solidi are clipped or diminished in size, or nibbled away, to use the proper term for such avarice, since some persons refuse to accept such solidi on the ground that they are light and inadequate. Therefore, it is Our pleasure to establish in each municipality an official called by the Greek word zygostates (lit. weigher), who by reason of his trustworthiness and vigilance will neither deceive nor be deceived, so that in accordance with his judgment and reliability he may settle any dispute that may arise between the seller and the buyer with respect to solidi. - Given on the ninth day before the kalends of May at Salona in the year of the fourth consulship of Julian Augustus and the consulship of Sallustius [= April 23, 363].' (Cod. Theod. XII.7,2).
The above passage describes the government official, who would have used a government issued weight. The Chi-Rho coin shown above is something that perhaps a local merchant would have made, to avoid having to go downtown to the official every time he had a suspect solidus.
3 of the coins below are also 4.3g, one is 4.4g and the Galeria Valeria is a little light at 4.2. The lighter weight of that coin can be accounted for because of corrosion.

Maxentius AE Nummus. Ostia, 312 BC. [IMP C MAXENTIVS P F AVG], laureate head right / [AETERNITAS AVG N], the Dioscuri standing facing each other, their horses between; [MOSTS] in exergue. Cf. RIC 35. 4.3g, 20mm

Maximianus
A.D. 308- 309
24mm 4.3g
GAL MAXIMIANVS P F AVG; laureate head right.
VIRTVTI E-XERCITVS; Mars advancing, naked but for flowing chlamys; right holding spear, left trophy over shoulder; in left field B
In ex. [MKV]
RIC VI Cyzicus 47

Galeria Valeria AD 293-311. Cyzicus
20mm 4.2 g

GLORIA ROMANORVM emperor reverse from Constantinople (circa A.D. 385) 19x20 4.4g

Unknown 21mm 4.3