What can I do to prevent leg ulcers from weeping?

Compression. Use compression stockings and dressings. This is critical. Elevate your legs as much as you can and walk. A vein specialist or phlebologist can treat you definitively. Use phlebology.Org for referral.
Leg ulcers. Leg ulcers that are weeping need clinical attention. There needs to be an assessment of the ulcers and their cause in order to development a plan that addresses the underlying pathophysiology. Please seek attention as soon as you can.
compression. Short term: adequate and properly applied compression will reduce the drainage and get the ulceraton to close faster. Long term: need to address the underlying pathology and take action to help prevent recurrances. Long term: compression stockings, regardless of having surgical intervention or not.