Eight weeks old is too young to let a child "cry it out." And I'm against the cry it out method, in general.
A child learns to self-soothe by being soothed by a parent. Here's an excellent article on the topic backed by research. It's worth reading if you're a parent or going to become a parent:
Dangers of Crying It Out: Damaging children and their relationships for the longterm
http://www.psychologytoday.com/blog/moral-landscapes/201112/dangers-crying-it-out
Someone on Huffington Post wrote this synopsis of the article...
In her recent piece for Psychology Today, Darcia Narvaez, an associate professor of psychology at Notre Dame, writes that when babies are stressed, their bodies release cortisol into their systems -- a toxic hormone that kills brain cells. Considering their brains are only 25 percent developed when they're born full-term and grow rapidly in their first year, killing off baby brain cells is a huge no bueno. Narvaez notes that studies out of Harvard, Yale, Baylor and other institutions show that said killing off of baby brain cells can lead to the higher probability of ADHD, poor academic performance and anti-social tendencies, and that human babies are hardwired for hands-on comfort and care.
"Babies are built to expect the equivalent of an 'external womb' after birth... being held constantly, breastfed on demand, needs met quickly," Narvaez writes. "These practices are known to facilitate good brain and body development. When babies display discomfort, it signals that a need is not getting met, a need of their rapidly growing systems."