At what age can babies be spoiled by holding them while sleeping? My 3-week-old often wakes up as soon as I lay her down.

Kids at this age are already actively trying to learn how to fall asleep and will begin to develop habits that help them to drift off to sleep. If you hold her while sleeping, she will probably come to expect that. I wouldn't call this spoiled at all, but a habit you may or may not want to encourage. For some families, the best choice is to sleep together. For others, teaching the baby to sleep independently is preferred. To do this, you want to look for opportunities when she is quite drowsy so you can lay her down almost asleep. If she rouses or awakens, often the best choice is to stay with her and to pat her gently but firmly to help her settle herself, without picking her back up. Of course, sometimes she will fall asleep other ways and that is fine. But you want to look for opportunities for her to learn.

Again, either way is fine. You don't have to do it either way. It is not spoiling, just building sleep habits. You can choose one way now and then switch later, although the switch often means a few long, exhausting weeks.