Suddenly (reading loosely related "related questions" on the right of the page) I came to the idea which after testing seems better than others.
I've used kitchen scales to measure the weight of the sheet. Then I used the ruler to calculate the area and vernier caliper (if it is proper translation for what we locally call "shtangentzirkule") to check the overall sheet thinkness roughly.
Then I calculate the expected weight of laminate and subtract it from the total weight. Now I have the weight of two copper sheets (in my case it was about
10g for area of about
160 cm2) so I get the answer (0.0069 cm for two sheets total) looking very close to 0.035 mm per sheet.
S - area of the sheet (163 cm3 in my case)
W - total weight of the sheet (55 g)
d - thickness of the sheet (0.14 cm)
p0 - laminate density (1.85 g / cm3) - googled, of course
p1 - copper density (9 g / cm3)
w0 = S * d * p0 (I get about 45.6 g)
w1 = W - w0 (i.e. 9g)
d0= w1 / (S * p1) / 2 layers
This should be bit less effective for single-side sheets, but I hope it will still work well, since the copper is almost 5 times more dense compared to the laminate...
Other ideas I have were either try to measure resistance or the time of solving in the FeCl or something like this. But I have no idea how to make them easy or reliable...