Airliners and Transports ("heavies)) usually have generous margins. They can readily make concessions within their larger "envelopes of flight parameters". Smaller planes probably don't.
All pilots are taught to do preflight planning. This is required by law.
All planes are designed to strict specifications. These specs are published, in Flight Manuals. This is required by law.
Preflight planning requires use of those Flight Manuals, which include applicable tables, worksheets for calculations and may specify use of the E6-B or other flight computing accessory.
As a PIC (Pilot In Command), I would be the "lawful master of such a vessel". Flight safety is a primary responsibility. On such a smaller craft, I would consider safety, physics (including theory of flight) and applicable regulations. I would have no compunction in grounding a 400 pound passenger, his 400 pound luggage or both.
If I were to accept a 300 pound passenger, I would retire to the pilots briefing room and replot my course and CG calculations; I would punch in new numbers for the takeoff roll and check those charts. If I had done all these the night before, I would do them again, upon seeing the passenger. I would not take on full fuel and would plan in shorter legs with more frequent fuel stops.
Nor would I apologize, for doing my clear and lawful duty.
Mustang