Overrun with Weeds!

To me there is not much difference planting plants in the gaps or letting weeds grow.
Maybe I'm a bit odd, don't answer that

It's paving and anything growing in the cracks will just look like weeds anyway.

 

I'd make a slight exception for crazy paving, I mean the name tends to suggest the owner is, well, slightly crazy.

But formal block paving, I'm not so sure.

 

As above, rake out weeds and roots. Maybe vac out with Henry or similar. Mix sharp sand and ordinary portland cement (1:10) dry, brush in, allow to dry few hours , brush away excess leaving a nominal drainage. No soil means no weeds . Maintain or repeat.