Welcome! I really don't consider my Toto a "tiny" but by some standards, I suppose she would be. She weighs slightly over 5 lbs. and is 8" tall and 8" long and came from an excellent show breeder. She will be 7 yrs. old on 7/18 and has been in perfect health her entire life. The only problem she has ever had, my husband and I caused. Her vet has always told us that due to her small bone structure, she should never, ever be allowed to weigh more than 3 to 3 1/2 lbs. She is so spoiled, it's very hard to refuse her anything, therefore, at one point she gained to around 6 lbs.!! Hubby is a "junk food junkie" and loves to share. He reached down to pick her up one night and she began screaming to the top of her lungs ... long story short, she had five of her little ribs seperate because of all the weight. Her tiny little frame just can't tolerate it but we can't get her below 5 lbs. We are very, very careful with her, she eats excellent food and I have reduced the quantity and she gets one "special" treat every day. [Kona's Chips and only one small strip of that.] Sorry this is long but just wanted you to know that there are indeed small Yorkies who are healthy and never have a problem!
Good luck with your baby!