Triac getting current from gate
If the triac does not turn on or the connection to MT2 is broken the resistor will heat up. Power will be >10W on 120V or >40W on 240V, so more than any small resistor can handle. 

By the way, your diac is doing nothing useful- only increasing the electrical noise and reducing the voltage to the load somewhat. 

Also the resistor value is rather high, again decreasing the load voltage and making it more asymmetrical (DC component), which can damage some types of loads (motors, compressors, transformers etc.)

A triac 'static switch' normally would comprise just the triac and a resistor of around 100-200 ohms. The resistor can be expected to burn up if the triac fails to trigger (eg. shorted MT1 to gate) or the MT2 connection is broken, so allow for that to happen safely, by using a flameproof resistor and ensuring it can't cause anything else nearby to burst into flames.