Can't help you with the Belchertown specifics, but assuming you want WeeWX to support l/m2 and l/m2/h for rain and rain rate, at a minimum you will need to add appropriate entries to
weewx.units.conversionDict. This cannot be done through
weewx.conf and needs to be done via some python code. This can be done in a number of ways, but in your case adding some entries to
extensions.py is probably easiest and quickest. You want something like step 4
here. Note that as you are adding a new unit to
group_rain and
group_rainrate you will need to add entries to the existing
conversionDict entries for each
group_rain and
group_rainrate unit, ie:
'mm', 'cm', 'inch', 'mm_per_hour', 'cm_per_hour' and 'inch_per_hour'.
You could also add default formats and unit labels for your new units to weewx.units.default_unit_format_dict and weewx.units.default_unit_label_dict respectively. This is not essential to use your new units in WeeWX reports and plots, not sure about Belchertown though.
Gary