MCP 3909 energy metering chip problem
The MCP3909 should always operate in pulse output mode by default. So the LEDs should toggle when the IC detects power
According to the data sheet (figure 1-1) Fout1/Fout0 create low-pulses and are active high, while HFout creates high-pulses

that's why the D2 and D3 are always on (Fout creates 275ms low-pulses, HFout creates 90ms high-pulses)

a 200 _micro_ohm current sense resistor is rather low for a 5A load. This results in a voltage drop of only 0.8mV. But the full scale voltage on the current channel is 440mV (see page 3) with a gain of 1


Lets calculate:


on the current channel, you get 1/500th of the full scale
on the voltage channel, you get 1/2 of the full scale
so the detected power is 1/1000 of the full scale
for Fout the frequency is, depending on the multiplier configuration, between 0.37 and 2.96 Hz for full power (when you are using a 3.58Mhz crystal as the data sheets suggests)
D2 and D3 toggle with 1/1000th of that - no wonder they are on always
HFout pulses, on full scale, with 27.1 or 47.42 Hz (depending on the configuration)
so with 1/1000th of that, you will get on small high-pulse every 25 of 50 seconds


So you should use a larger current sense resistor. For a load of 4A, about 100 _milli_ohm would be OK, then would be near full scale on the current channel.

Regarding the 0.5V you measure for the voltage reference: is this with the MCU attached? It should be 2.4V - maybe you have a short (or an unclean solder joint) there?