It sounds like she might be a little off with her date, you have seen a good strong gheart beat so relax and enjoy. The size of the sac is not really relevant i dont think
I have only heard of one person whose sac was measuring small but the baby was measuring right on track. The next week, the sac had caught up. Try not to worry too much. The hb is great.
A heart rate of 165 sounds good. Obviously, the amniotic sac can't be smaller than the embryo. Are you saying the sac is measuring smaller than expected for the date? Or that the baby is?