Here is an altered coin of Decentius from Lyon. Not surprisingly, since Magnentius and Decentius lost, the bust and name is mostly erased. The mintmark is also missing, but it is either RIC VIII Lyons 171, 173, or 175. This coin weighs 4.34 grams and it seems likely it was made to use as a solidus weight. A solidus ideally weighs about 4.5 grams, but some are underweight because of clipping; which is why people made weights, to make sure that the gold coins were in a tolerable weight range. These weights occasionally turn up for sale, you can find more information if you search for exagium.
'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 reliabilty 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 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.
RIC VIII gives the average weight for this S-✶ Chi-Rho series at 4.46 grams, but this coin was originally a bit heavier, given the amount of material removed. Bastien records weights for individual coins and the lowest weight for this series for Decentius is 4.27 grams and the highest is 6.85 grams, a weight which would have worked nicely to make a similar 4.34 grams weight.
Sometimes coins will turn up that have been similarly altered which are usually described as game pieces or tokens, but the weight of this Chi-Rho coin, being so close to a solidus, seems like too much of a coincidence for it to not have been intended as a weight.
