For example, Why is Imperial Germany (1871-1918) considered the second reich but the weimar republic is not?
Post WW2 of course there is not mainstream support for considering Germany as it stands today to be a fourth Reich as it has connotations with Nazi/fascist rule, but with past distinct periods in German history why are some considered Reichs while others are not? Is a Reich determined when the leader of Germany at a given period dubs the era a Reich or it is retroactively given the title when analyzing it's history?
'Reich' is German for 'Empire' so the term has really only applied to periods of German Imperial ambition. The idea of 'numbered' Reichen really only arises as a result of Nazi propaganda. To whit; the 'First Reich' was the Holy Roman Empire, and the 'Second Reich' was the German Empire of 1872-1919. This was the basis for the Nazi government proclaiming a 'Third Reich' as much of their electoral rhetoric was framed around reclaiming the lost Imperial glory of the German Empire that they alleged had been surrendered at Versailles.
The Weimar Republic couldn't be considered a 'Reich' since Germany lost what overseas lands it had as well as a considerable amount of its European territories in the wake of the Great War.