Standard deviation of Likelihood - sample size dependent?

Thank you so much for answering @ricardoV94 and @AlexAndorra. It makes a lot of sense, and i am embarrased it wasnt obvious in the first place, heh.

I have problems with two observations depending on my confidence in my prior mean(?). If i set the sd of the prior mean to be 0.01 it seems to be ok, if i set it to be 1 or two, i am having divergencies.