Did you ever see such a set? Bishop unusual...

https://www.ricardo.ch/de/a/1273287522

I couldn't find any information about this specific set. In his website Holger Langer describes a set which is also very heavy and with an unusual bishop. Not exactly like this one, but the weight and bishops are similar features. Anyway, I hope someone will recognise my set. Thanks.

I haven’t seen a set exactly like that, but I have seen some sets featuring bishops with hats. Below is a c. 1890 set presumed to be of German origin, from a page of the book Master Pieces by Gareth Williams. I guess this may hint at a German convention of bishops with cute little hats—although I certainly haven’t seen it often.

Bishops with hats or feathers were often seen in Biedermeier coffee house sets and in the transition towards Vienna coffee house sets, see below (pictures from my book):

However, from the style of the other pieces in your set, I think that this is not an early or mid 19th century set. The rest of the pieces is too far off compared to Biedermeier sets, in particular the rather fleshy knights, the rooks, but also the kings with cross finials etc. My gut feeling tells me it is rather more early 20th century, so probably 1900-1930's. But this is just an educated guess, no more.