ISS' JEM-ELM-PS' rigid module structure weighs about 6 tons empty for 55 m³ pressurized space plus 2.4 tons for the 8 mounted racks (structure ~110 kg/m³), which compares very favourably with BEAM's 3.0 tons for 16 cubic meters (188 kg/m³).
Payload fairings on rockets are mostly standardized - partly because the aerodynamic calculations for pressure on it are complicated enough that it'd be insane to adapt fairings for individual payloads; this is even more the case nowadays where you want to save some money. In fact, e.g. for Ariane 5 there's only a single type of payload fairing being used - there were two designed. It's the same with pretty much all current launchers.
The full-size BA330 modules that Bigelow still has on their design tables which don't really have a chance of ever launching are a different matter. These are basically designed to take up the space and weight that a "full-size" module (about 15-20 tons) transportable by typical rockets would take up, and then expand into modules with an internal volume one-quarter of the entire ISS.
Most of the (accessible) pressurized space within the station isn't crew space anyway btw. About one third of the volume is the free central corridors within a module; the other two thirds are taken up by rack space and fixed-mounted equipment. The standard solution to creating more "private quarters" - back when there were occasinally more people onboard than the 3-6 now - to take an unused rack space section and clip a sheet over its corridor side (kinda like
this, on the left). That went well enough that since 2008 there's now a couple specialized "crew quarter racks" onboard which look like
this (the two sections in front are the door panels to the corridor that can be closed). These are pretty much identical in size to the two private quarters in the Russian section btw (which are a bit better in that they have a small window). It definitely beats sleeping like
this.
