My yorkie at 4.5 months was weighed in at 4.12 lbs at time of chipping.
My late shihtzu was tattooed before I got her as she was 3-5 yrs old and already spayed. She probably had it done the most ancient way possible as it must have been over a decade ago when the procedure was done. My dog before that went through life without either of those as it must have been before the age of microchipping.
My brother's cat was tattooed as a kitten but didn't show any signs of it bothering her at all, however, cats are supposedly good at hiding pain and discomfort. I opted not to tattoo or chip my indoor cat when she was spayed. I am still not comfortable with placing foreign object(s) in my baby but I figured I'd regret it more if I had no real means to ID her if/when she's stolen or lost.
Tattooing wouldn't be very secure when it comes to theft, but works alright for general identifying purposes. As for pain/discomfort, I really don't know. I don't have any tattoos on myself so I can't even speak from experience. My sister did feel discomfort initially when she got a tattoo on her shoulder years ago with a needle from a tattoo salon. A friend's friend was promoting laser eyeliner tattooing during a stagette. Her sister got it done 7 years ago and it's only now pretty much faded. She just got it done an hour before we met up for the stagette and was as chirpy as usual and the little bit of discomfort/stinging she felt before hand has totally faded by then. So if the "ouchless" tattooing method is done by laser... I wouldn't be surprised if it might very well be ouchless, just that a human might have a higher tolerance level for discomfort than a little puppy... but I'd think the eyeline would be more sensitive than a dog's ear?
Until there is proof of ill side-effects from my own experience or from people around me, I would still opt for microchipping for ease of mind and a bonus for more shallow people like myself is, you don't get an ugly tattoo in your pretty little baby's ear/thigh/belly although it can be covered up by hair...