My first tip is to change your brush. Different types of bristles take in different amounts of waters. Rule of thumb, real hair takes up more water than synthetic, softer brushes more than stiff. Synthetic or real, squirrel takes up the most water. Kolinsky sable the next, and hog bristles take up almost none. Brushes formulated for oil take up less than those formulated for watercolor and acrylic, those formulated for acrylic less those for watercolor. Some brands, like Princeton, rate their brushes at their site.
I switch my brushes according to whether I want really loose, flowing effect (squirrel, synthetic) or harder, crisp edges (Kolinsky, synthetic).
Use pan paints. They are harder to get really liquid paint and so easier to avoid overloading your brush. I prefer pan paint because they are less messy, and I choose my brush according to how much water it will hold, using it for the effect-loose or crisp, that I want.
If you don’t want to change brushes or use pan paints, then try mixing your paint with water before you start painting, and experiment to get the ratio that flows without overloading your brush. Watercolor really is about the control of water to paint. Sometimes you want pure liquid, other times you want thick cream or somewhere in between.
I hope that helps.