Potatoes lose weight when placed in high concentration sucrose solutions because they lose water through osmosis. Osmosis is the process where solvent molecules pass through semi-permeable membranes to equalize the solute concentration on both sides of the membrane.
Living organisms contain water in their cells, including potatoes. Cell membranes are semi-permeable membranes that allow water to pass through readily.
If the cells are placed in a hypertonic solution, they lose water and shrivel. Since water is quite dense, they also lose mass. The water loss is in proportion to the concentration of the solution. This same process is used to create pickles from cucumbers.