A nice little problem. I got this Roman coin from a Frank Robinson cheap lot. Although it's very worn, it is large and attractive and with a bust on both sides (no BD, the green is stable). The one on the obverse looks like Caracalla or Elagabalus. A friend said: Macrinus, but I don't see a beard on this broad head, maybe a stubble beard. The one on the reverse looks like a young person. It's 33 mm and 19.51 gr. Can you help?
The size and the portrait style suggests a provincial of Caracalla from Tarsus in Cilicia. Reverse I would guess Julia Domna rather than Plautilla.
Thanks for the hint of Tarsus, @zumbly! RPC online has large Tarsus AEs of Elagabalus, one with Julia Paula, but the ones in RPC are all significantly lighter (mine is of a thick type). For Caracalla I checked ACSearch, and there are some Domnas of the right weight. I noticed that the average condition of these heavy bronzes (a.o. on VCoins) is something like VG, so mine is not too bad after all. But I also have the sylloge catalog of Tahberer on my computer, Ancient Cilician Coins of the Collection of B. Tahberer (2014), a Canadian collector. It is in English and Turkish and counts about 1800 coins, with weight and diameter (Thank you, Mr Tahberer!) and many excellent photos. Here are nrs. 1511 and 1512, of Julia Domna. On my coin you can see the crescent under Domna's bust and the π (Pi) to the right of Caracalla. Both coins are 3.5 gr. lighter, but they are a bit chipped.
I think you've got it. A search on ISEGRIM also shows the type catalogued in BMC, SNG Levante and SNG France. The weights of the examples cited in Levante and France are close to yours.
