A weed will not grow where another plant is,if you start putting grass seed or plants they will stop due to lack of space, its a wild idea but try it

Something like 'pathclear' maybe worth a try, not until the weeds are growing though, at this time of year the poison wouldn't be absorbed by the weeds, leave it until its warmer

or it means having it all redone either with slabs or block paving, even using a weed supressant membrane under the gravel stops weed coming up, but not the seeds germinating

My front garden is used for parking and wheelie bins so only have two small borders, the rest is part slabs with granite in other places, pots and troughs for decorative purposes, I have been plagued with groundelder and mares tail for more years than I care to remember, its rampant in my neighbours garden, tried every weedkiller I can but although I manage to kill it off, it returns every year with a vengeance, now I use salt and find it works as well as any expensive weedkillers, not recommended on anywhere I want to grow plants but does for my driveway also saves me many hours of backbending, frustration and money.

Gravel really needs to be several inches thick to stop weeds coming through - the depth stops the seeds getting down to the soil and cuts out the light.
The expense of moving may have left your wallet feeling battered but it would probably be worth the cost of having the area properly paved, maybe with a couple of raised beds built so that you have some area for plants that you can reach comfortably.

Pathclear says on the pack that it is supposed to remain effecive for 6 months. If you do decide on using a weedkiller you need one that affects the soil rather than just acting though the leaves.

A weed is just a plant in the wrong place so the advice from Wildlifeb will not be any help.
Do you know which plants they are that are coming up through the gravel. This will be important in the long term solution. Glyphosphate and pathclear usually work on most herbaceous weeds. If it is marestails then it will be more difficult to sort.

The weed problem will continue unless you make a major alteration. You would need to get someone to take up all the stones, peg down some heavy landscaping material and then replace a small layer of the stones. By doing this, any weeds that start to germinate will have nowhere to root and will quickly die off. Yes, it might cost you in the short term, but you won't have to keep buying and applying weedkiller and will still be cheaper than slabbing the site.

Rae, I suggested changing to paving as a long-term option because gravel that is deep enough to stop the weeds can get very difficult to walk on as you get older. You know how well you're getting about at the moment but think ahead 5 or 10 years (I know my mother came to regret having her driveway gravelled instead of paved, simply because it became like walking on shifting sand as she got into her 90s - and it was a nightmare wheeling the multitude of recycling/dustbins over it).

Either way the ground will need to be properly prepared and won't be cheap but I think switching over to paving would be more cost effective in the long run.

In my gravelled area plants keep self-seeding and i pull them out. It seems to me that whatever you do, debris will build up in the gravel providing a growing medium for many many plants. If you can kill them with what Seaburngirl suggests then problem solved but I agree that a paved area will provide a permanent work-free solution.