If you are paddling flat water then I'd suggest getting a flat water shape, not a surf one. They make paddling a lot nicer and less tiring. There are a few shorter flat water touring style boards around these days - you don't have to go to 12'6".
Maybe a Starboard GO Takhine?
Or maybe something like the Surftech Chameleon?
None of these sorts of boards are particularly light however, even when they are marketed at women. But they aren't heavy either, and by using a trolley or similar (eg. the SUP Mule) for long distances there's usually a workaround.
Hope this helps.