A weeping beech is one of the most striking trees in the garden. Its long branches droop down, forming a swinging skirt that drapes the trunk. When the tree is properly pruned, the sun can filter though the small rounded leaves and light the hidden center. The very worst way to prune weeping beech is to crop these delicate branches like bangs on a woman's forehead. It will take a long time for the weeping beech to recover from that. The better way is to work down from the top of the tree and out from the inside, working with the weeping beech to find its perfect shape.
Completely cut out branches that are growing close to the trunk and straight down. Work out from the trunk pruning away those branches that are creating a tangle. Create a clear, open umbrella-like space around the trunk. When finished, you should be able to walk without bumping into branches overhead.
Remove any crossing branches found throughout the tree. These can rub against each other and damage each other or make the branches vulnerable to disease. Be careful not to harm the branch you leave when you cut away the crossing branch. You should be able to see them now that you have cleared from beneath.
Remove several outside branches from the top of the tree as well if the tree is very tall or very full. If there are many of these, choose one or two from each side of the tree, keeping it symmetrical. Also choose any that look half dead, very old or disproportionately thick or thin.
Trim branches that touch the ground because they may root where they touch. When trimmed lightly they should spring up toward the sun. This will keep them from gathering vermin or fungus from the ground. The leafy branches in the following season will sway more gracefully as well.
Clear away all debris, and water the weeping beech deeply. Fallen leaves can mulch the tree or you can mulch with another material such as wood chips. Spread the mulch inside the drip line (the area of the ground defined by the horizontal extent of the branch overhang).