Seems it is like a little clovery plant that puts out runners and fires its seeds from little pods. Perhaps soak the pot well with water, then carefully extract the rather deep roots. Go as far down as you dare and then fill with fresh compost. It is a very pervasive little thug. It seems a shame not to take your Acer with you because of this tiny invader.

I wonder if you have Ranunculus ficaria 'Coy Hussey' or perhaps an Oxalis? I would be inclined to try and identify this weed! to help you decide if its worth the risk?
I would have thought in a pot you could remove the weed whenever you see it and eventually it would be so weak it would die. The danger is if you let it set seed or plant the whole thing in the garden.

Why not re-pot the acer in fresh compost? Remove as much of the soil as possible from the roots and leave it for the new occupants of this home.

I'd put money on it being Oxalis. We had such a serious problem with it on some beds on Brighton seafront that they had the soil removed new sterilised stuff put and left bare for a year....and it still came back. You need to get those roots out !!!

Thank you all so much for your kind advice which is a great help and very much appreciated.

I would also get rid of most of the soil and add fresh compost. The Acer will be heading for hibernation in a few weeks anyway so it will not do any harm, fresh soil will be beneficial.

Don't forget to use ericaceous compost for best results if you replenish the soil.

Many, many thanks again dear folks. Your good advice will all be heeded. Sadly I do not possess greenfingers so wish my little Acer luck - it will need it! It is only thanks to that little Oxalis weed that I discovered the tree needs to have her roots protectively covered so between the weed and the pebbles I now have covering the top of the pot little Acer not only looks beautifully fresh and green all year also now the leaves turn a lovely orange colour in the autumn. Shame the Oxalis weed is so aggressively invasive as I did at first think it very prettily enhanced the whole thing.

It seems almost impossible to eradicate it completely - it came with me to Wales from Staffordshire, and regularly pops up even in pots in the conservatory. You may feel a bit more kindly towards it if you call it by its country name of Sleeping Beauty---and then again, perhaps not---