Well, in German for a possessive it would need an apostrophe to be fully correct, because it already ends on an s-sound. In general in German we don't do 's for the possessive but just an s at the end of names (though English influence has led to liberal apostrophe sprinkling), but if a name already ends on an s, ß, or z you don't write a second s but just an apostrophe, and the name doesn't sound any different, for example "Hans' Haus". In spoken German you sometimes hear it like "Hanses Haus" so some people spell then "Hans's Haus" but that's not how you are supposed to write. So it should be written Weiß' Kreuz if it was meant that way, but it sounds like the possessive.

And I'm fairly sure that the usage of Kreuz for a burden comes from Christianity just like the English "it's his cross to bear" etc. but afaik the most common German usage eith that is "es ist ein Kreuz mit..." (literally "it is a cross with...") for something or someone being difficult, obstructive or obnoxious and generally hard to bear, so the image there isn't directly somebody carrying a cross around (though that saying also exists), and these days most people might even equally think of lower backpain, because Kreuz also means the lumbar region.