(230V - 3V) / 20kOhm = 10mA This is why the led is only dim.
My theory for the Voltage across the LED is that it is in fact the multimeter that is taking an average of the DC/AC components, because as previously stated your circuit is a half bridge. The led is only on half the time which makes the 10mA seem like 5mA. When a diode is reverse biased it sees the whole 223 volts or 122V. Perhaps the multimeter is showing some weird average. The 50-60Hz of half the wave must be messing with the calculations.
Try this, another led in parallel with that led but hooked up in reverse with respect to this one, they should both look dim, and if you put the multimeter across the terminal now in DC mode it will maybe show 3V....just a guess from an amateur
Mike