What mizinamo is trying to show is the etymology of the word to help you with other words that might have the same prefix. "συν" in general means "together" as we say "connect", "cooperate" "contribute" and many others which in Greeκ all use συν. I don't see any mention of the word "unequally...". There is nothing more complex.
At first, I thought the same thing- then I noticed a pattern: In Greek, proparoxytones become secondarily oxytone when followed by a genitive enclitic. More simply put, words that are stressed on the third to last syllable acquire an extra stress on the last syllable when they are "possessed." So...o/η σύζυγος (the husband/wife) becomes ο/η σύζυγός μου (my husband/wife). Similarly, το αυτοκίνητο (the car) become το αυτοκίνητό σου (your car).
Edit: I just saw that jaye16 responded and his/her explanation probably makes more sense than mine.
It's one of the exceptions, but a rather logical one. When a word is accented on the third syllable from the end and is followed be a word with no accent: μου, my, της - her etc you then have four syllables pronounced as one word.
It doesn't exactly roll off the tongue. So we accent the last syllable of the noun to make it smoother. Both accented syllables are stressed.
So, with only one accent you have: o SI zi gos mu
but with the extra accent you get: o SI zi GOS mu. Hope this helps any questions just ask.