My bet is Isaac II Angelus, SB 2003. Sometimes the akakia can look a bit weird, as it does here. On the right above his shoulder is the manus dei. (I'm not at all sure about this ID, though.) The akakia is a neat accoutrement... it was a roll of purple silk containing dust, a symbol of humanity's mortality.
maybe "latin rules" as well? these are pretty dang hard to ID. here is one of mine. Latin Empire of Constantinople. A.D. 1204-1261. small module trachy (21 mm, 1.8 g). Christ standing facing / Emperor standing facing with labarum and orb. SB 2035. Constantinople.
Theodore I Comnenus-Lascaris. Emperor of Nicaea, 1208-1222. BI Trachy. Nicaea mint. Christ Pantokrator enthroned facing / Theodore standing facing, holding cruciform scepter and akakia; star to lower left (faintly visible). DOC 6.2 var. (star to lower right on rev.); SB 2062. https://www.cngcoins.com/Coin.aspx?CoinID=241806
Here's one of my unidentified Byzantine. I think it's from the 11th century? Does anybody know? Obverse, bust of emperor or christ facing. Reverse, cross on steps.
What's the weight? It'll be a tetarteron or half-tetarteron of Alexius I, Manuel I, or (just possibly) John II. Looks like an IC XC around the cross, which I think would mean Manuel.
I don't have a scale but I'd guess around 4 gm. Manuel - that takes us back to the time of the crusades. He was cast as a villain in the book The Journey of Louis VII to the East by Odo of Deuil. https://en.wikipedia.org/wiki/Odo_of_Deuil