I've been researching a bit and trying to figure out which sets of world circulating coins get proportionally larger with an increase in face value.
The one I am familiar with are the US pre-1964 dimes, quarters, and half dollars. Where the dime is 2.5 grams, a quarter dollar being 2.5-times as valuable weighs 2.5-times as much (6.25 grams), and the half dollar being 5-times as valuable weighs 5-times as much (12.5 grams). The dollar however rather than being 10x the weight of a dime is close to 10.7-times the weight.
The coins of the Swiss Franc before 1967 and the French Franc before 1920 are valued/weighed similarly; those being .5, 1, and 2 Francs weighed 2.5, 5, and 10 grams respectively.
The coins of the UK either .925 before 1926 or .500 before 1936 were also weight/value proportionate, 3 pence weighed 1.41 grams, a 6p 2.83g, a 1 Shilling (12p) 5.65g, 1 Florin (24p) 11.31g, 1/2 Crown (valued at 2 shilling and 6 pence, or equal to 30 pence) weighed in at 10 times the 3 pence or 14.14g, and the Crown at 28.28g
Other Commonwealth (Australia, NZ, Canada, etc) had similar weight to value proportionate coins as well. Australia and NZ were more like the UK where Canada being more similar to that of the US.
What other countries did this?
the 2.5, 5 gram 23mm, and 10 gram 27mm standards were used widely prior to 1920 or so.
all of the countries in the Latin Monetary Union from 1865 until the 1920s used them -
besides France and Switzerland, as you mentioned, also Belgium, Italy, Spain, Greece, Albania, Serbia, Bulgaria, and others used this format.
In South America you will find the same sizes for 10cent, 20cent, and 40cent, for example Cuba https://en.numista.com/catalogue/pieces3014.html et seq.
Colombia https://en.numista.com/catalogue/pieces25414.html
Uruguay https://en.numista.com/catalogue/pieces4360.html
For some time Uruguay coins were minted in Paris.
Venezuela too, maybe others.
Jamais l'or n'a perdu la plus petite occasion de se montrer stupide. -Balzac
This proportionality was rather rule than exception until a hundred years ago, as most currencies were linked to gold or silver and coins represented their value in metal. In some cases this weight proportionality can still be observed in modern coins. For example, dimes and quarters still have the same size as a century ago but only the silver was replaced by copper-nickel which is about 100 times cheaper and lasts longer.
