Good luck in your search
I thought I wanted a 'tiny 3 lb yorkie too' and when I got TJ and Roxy I was told they would stay small...Well, 4 years later Roxy is 5 lbs. 3 oz. and TJ is 7 lbs 3 oz - They are PERFECT! Honestly, they are still petite and small - yet I don't have to worry about the them getting hurt or stepped on, etc...AND if we were ever to have kids, they are at a perfect weight and size - very kid friendly.
I suggest finding a reputable breeder, but don't pass up one just bc the adult weight should be 5 or 5.5 lbs - Trust me, it's still small