The only thing I use that's weight-aware is Strava. It understands that I weigh X and the bikes weigh whatever they weigh. Annoyingly, it has no concept of luggage, to go with its non-concept of various common types of cycle and it's non-concept of the Garmin eTrex series.
I've fudged the bike weight upwards a bit to allow for the bare minimum of luggage that I'm likely to be carrying, and accept that it will under-read when I've got a touring or utility load. It doesn't really matter, because its estimates are basically useless anyway, as it fails to allow for the aero and rolling characteristics of different bikes (it thinks I work harder on the recumbent than on the Brompton, for example).
More generally, I agree that gross weight is what matters, but it's likely that a cycling-oriented HRM will incorporate some sort of 'standard bike' fudge factor into its calculations already...