PWM-driven MOSFET heats up

I have designed an MCU-based PWM dimmer for LED strips.

My circuit works fine but there is a problem: The MOSFET is unexpectedly hot (i.e. 65°C). So I scoped the drain voltage using an oscilloscope and I saw that the drain voltage was about 0.130V (as expected) when the MOSFET is on, but it is 9V --it should be 16V-- when the MOSFET is off. So I'm not sure but I think that this causes the MOSFET to heat up.

^{simulate this circuit – Schematic created using CircuitLab}

Where is my fault? How can I solve this problem?

EDIT: Here are the waveform of V_DS:

Answer

The 9 volts is a red herring. 0.13 volts across a FET of on-resistance of 0.05 ohms is a power of 340 mW and this will generate heat. The junction to ambient thermal resistance is typically 50 K/W, so without a heat sink and at a local ambient temperature of 30 °C, the temperature will rise to 30 °C + 0.34 W * 50 K/W = 47 °C then factor in that the temperature rise might locally increase ambient another twenty degrees and you are at 67 °C. Not really a problem.