If the master frame is grown to 140 pixels wide, then there are 40 extra pixels. If each column has weight 1, then each column gets an equal share of the extra space, or 10 more pixels. Now suppose column 0 has weight 0, columns 1 and 2 have weight 1, and column 3 has weight 2. Column 0 will not grow, columns 1 and 2 will get 10 more pixels, and column 3 will get 20 more pixels. In most cases, weights of 0 or 1 make the most sense.
Weight works in reverse when shrinking.
If a row or column has to shrink, the weights are applied in reverse. A row or column with a higher weight will shrink more. For example, put two equal sized frames in columns with different weights. When the user makes the window bigger, the frame in the column with more weight gets larger more quickly. When the window is made smaller, that frame gets smaller more quickly.