The Brew Cabin

My driveway was blockpaved about 6 years ago. It is still performing well and generally looking good. I treat it twice a year with a wet and forget product to try to keep moss and algae at bay and occasional top up of kiln dried sand. However, the part of the drive which requires the most attention and effort are the edges. Where the block paving meets the public pavement and my side fences/walls there is a gap of about 1 inch which was finished with a weak mix mortar. This has deteriorated over the years and now requires me to clear weeds throughout the growing season.

I'm looking for advice on how to solve this issue e.g. would I need to remove all the old weak mix and replenish with a new weak mix mortar every few years or if there is a modern alternative that could be used instead.