The VERT_LOOP message is helpfull when tuning the vertical loop. You should have a look at z_sp (altitude setpoint) and z_ref (altitude reference = setpoint filtered by reference generator) to check that the values are fine. You may also use some saturations in reference generator in order to smooth the reference, in GUIDANCE_V section of the airframe configuration file:
<define name="REF_MIN_ZDD" value="-3"/>
<define name="REF_MAX_ZDD" value=" 3"/>
<define name="REF_MIN_ZD" value="-1.5"/>
<define name="REF_MAX_ZD" value=" 1.5"/>
Once you have checked that your reference is fine, (smooth, without discontinuities), that your altitude measurement is OK, then you cane tune the PID.