This sounds easy: use a mechanical switch attached to a lever or similar. The weight pushes the lever (or pulls on it), lever moves, switch closes. Use a counterweigth or spring to adjust sensitivity
How much do you want to go in the design process.
You could use a load cell, they a couple of $ on ebay.
If you want to control the degree of heat.
See Microchip MCP3421 weight scale app includes software.
For simple heat on/off use a load cell and set a comparitor to detect if for a certain level output of the L.C.
Then use a SSR to turn the heater on.
M.