Ulrich,
There aren't really any old courses that aren't royal. R. Zoute is good, but there are close runners up in Royal Antwerp and Royal Belgique. However, I don't think you'll get on either of these at a weekend unless you can arrange it in advance. I'd say your best bet would be to try R Hainault which is a very welcoming club and not far from Brussels. There are 27 holes (9 newish ones in genuine heathland by Hawtree). It could do with a tree clear out but is at least oldish (1933). R Waterloo is very dull. Farther afield it might be worth enquring in advance of the Simpson courses near Liege, R Sart-Tilman and RGC des Fagnes. Two courses in the west are Royal Latem (pretty routine and flat, but very friendly) and R Ostende (part links, but some very ordinary holes inland - makeshift). Bercuit is the oldest of the new generation of Belgian courses (RTJ 1965) but I could not in any way recommend it. There are some good holes amongst the 36 at Ch de la Tournette and plenty of ordinary ones, but it does at least offer a weekend green fee rate. Note that Friday often counts as weekend in Belgium. My advice would be to make sure you can take advantage of the dining rooms at lunchtime - I've had exceptionally good food at R Belgique, R Sart-Tilman and Ch de la Tournette - but as I was driving I had to forego the wine lists which made inspiring reading - a good run of Drouhin burgundies at Sart-Tilman, for example. If you are in Antwerp in the evening make sure to book at the Dock's cafe - excellent seafood.