Anne - It's easier the second time. My first one warped because of too much glue, I think, but I am suspicious that you caused your to warp just to make me feel better.
Waddie - I am using 67 pound Neenah Bright White premium cardstock. It is 0.19mm thick and seems to be working out just fine for these builds.
If you want really fine paper, I recommend going to Blick art supply and buying a pad of Borden & Riley #234 Paris Bleedproof paper for pens.
Borden & Riley Paris Bleedproof Paper For Pens - BLICK art materials
It is also about 0.19mm thick. If you buy the 9x12" book of 40 sheets, you can slice 1/2" off the right side and you have something close to A4 paper for models that come in that size. Some printers will accept the 9x12 sheets without modification. It is expensive, but lovely to work with. You can use the Neenah for most models and save the Borden & Riley for special projects.
Don