Katy we use our bikes in much the same way. I take mine out in all weathers but if you can avoid cold and high winds that'll reduce the weather factor and hence weight.
If you have to carry a charger (can't leave one at a destination) that's half a kilo. For light weight we should probably design around your everyday needs and you take an extra battery (spendy) when camping.
Do they generally let you take the battery in or do you run a long extension through a window? I made one up with a tough sleeve for that. Do customers ever freak out and what do you say to them?
On long, multiday trips, charging time is critical, so my gear is preorganised to get started asap. Most people won't need to go this far!
A four way short extension lead with my two chargers plugged in one side, and two USB-c chargers the other for camera and phone, all leads tidy and secured with velcro straps. 4.6A chargers, not the basic 1.8A. Time matters.
I carry in my two batteries, and the charger bundle, and ask for permission to 'charge while I have a meal and a pot of tea', never just 'can I charge, please'. There's a decent payout for them, which dwarfs the electricity cost.
My gear is all bonafide Shimano, clean, undamaged and with reassuring manufacturer's labelling. I have only been challenged once on safety grounds, and that was sufficient explanation as to why it was safe.
I only need charging in the 'winter' half of the year, and my riding is in the north and west, so I am not 'in the way' at busy times in busy places.
But the main key to success is accepting that 'no' is a perfectly reasonable answer, making that clear at the outset and just being polite. I have been charged for charging once, by a formidable Scottish cafe proprietor, but only had a refusal when no power point was available, or a junior staff member was unsure and the manager was not available.
Over time I have acquired local knowledge of charging locations on the routes I have used, and confidence that there is always an answer to be found.
Customers and indeed staff are generally interested or amazed at the very idea of an ebike on a journey of hundreds of miles, so helpful rather than worried.