Joints between paving stones - A breeding ground for weeds. Sustainable control?
From the picture you already have your patio installed.
To implement the polymetric sand solution or the mortar solution requires that you 


Pull up the pavers
Clean out the sand/dirt between the cracks
Reinstall the pavers
Apply polymetric sand/mortar


I've been working on the same issue but I am trying to not pull up the pavers.

The Problem:


Dirt gets into the cracks between the pavers
Seeds blow onto the patio and get into the dirt
Seeds grow and send roots down between the pavers


So, polymetric sand/mortar provides less opportunity for dirt which reduces the chance for seeds to sprout.

Putting weed blocker under the patio fails to address the root cause.

My Solution

I know I'm going to catch some heat for this but here goes.
I have a large paver patio and I hate pulling weeds so I decided to try salt to prevent weeds. Salt gets down into the cracks and makes an unfavorable environment for seeds to sprout.


Bought a 20 pound bag of table salt for $7 (not rock salt, table salt is super ground super fine)
Poured about 3 pounds of it onto the patio
Used a push broom to work the salt into the cracks. Since it was table salt it is very fine and broomed into the cracks nicely.
Using my water hose I wetted down the salt so that it washed into the cracks. Not a major hose down, just enough to get the salt wet and further into the cracks.


The patio looked a little salty for a few days. A rain or two brought the patio back to it's normal color.

The result


Weed free patio all summer
No salt damage to the pavers


If weeds start to grow again I'll broom in more salt. I'm one year into my experiment - so far, so good.