I am on very heavy South London clay, but over the years I have improved it, I hope. I don't formally dig it over. Each year when planting out bedding I make quite a large hole for each plant with a trowel and fill it with high quality multi-purpose compost. Thus each plant is in its own mini-environment. Over the years the topsoil has become less clayey, to the extent that the flower borders are now about 6 inches higher than the lawn.
This year I've tried Miracle-Gro for the first time and it really seems to have made a difference.
I even managed by digging in several hundred litres of ericaceous into one particular corner to plant 2 rhododendrons which have been successful for 3 years so far.
For weeding, just rough around the weeds' roots with a long-handled hoe.