I can't understand "beziehungsweise" in the context of its two parts, "beziehen" and "weise".
What is the logic behind its meaning?
The trick that leads us to understand the logic of "beziehungsweise" is knowing that the first part is not derived from the verb "beziehen" (to refer to) but from the noun "Beziehung".
If we translate "Beziehung" with "respect" then building an adverb with the suffix "-weise" follows a similar logic in English, and in German:
It's not really helpful to seek a direct translation for 'beziehungsweise', because it's more of a stylistic tic than anything. Takkat's comparison with 'respectively' is correct, but the only times I've seen 'respectively' used that way in English is as a translation of 'beziehungsweise', where the idiomatic English would really be 'or', or occasionally 'or, where appropriate,'.
Idiomatic uses of 'respectively' in English are in my opinion limited to cases where the speaker is aligning two lists: 'junior, intermediate and senior generals have one, two or three stars respectively'.