It was all Romeo and Juliet and balconies. What does ‘balconies’ mean？

The writer is referencing the famous scene in Shakespeare's play Romeo and Juliet when the lovers are physically separated by a balcony. They can see each other but cannot come together because of reasons beyond their control:

Many thanks！

I'd baulk at one.

The expression means that they could never be together; they had a relationship from a distance. So their love was like Romeo and Juliet's - forbidden.