Aneurysm - At What Size Does it become "Dangerous"?

I've been seeing a lot more of the heart surgeon lately, and they've taken many many blood samples. I just got done this morning doing a "sleep study" because I guess they also think I have sleep apnea, and a lowering of my blood pressure and respiration while asleep. All of these things combined do not make me feel very comfortable with this condition, but naturally the doctor is telling me "not to worry". Meanwhile they have me on "anti-anxiety" and "anti-depressant" meds..... more than likely to abate my worrying. The aneurysm has grown over 1.1 cm in about a year's time it is now 4.1 cm. Any input would be helpful. I've read a bunch on Web MD, and it kind of conflicts with my doctor telling me "not to worry".