The size on the Augustus coin (number 2) is approximately correct. Mine is 1.7g and 13mm, The Portia coin presented on wildwinds does not give the measurement only the weight at 1.19g, but the example on acsearch that I linked to yesterday has the measurement as 13.1mm. So, this coin (coin 1) is in the correct proximity as well.
I believe both your first two coins to be genuine; however, I will add that I put a lot of stock in what some of the others believe. If I were you, I would take these coins to an Ancients dealer for further examination. Good luck, and, btw, your doctor is correct. If you lose a couple of grams you'll feel much healtheir.
