"Why is my 3 week old fighting sleep and nursing all day long? A friend suggested 'The Wonder Weeks' by Dr. Sears - is there any validity to this?"
The Wonder Weeks is the English translation of Frans X Plooij's (Dutch) book. While great in theory, it has been disproven time and again (including by other professors and scholars who worked with him). Dr. Sears' work is fantastic, but he has nothing to do with Plooij or his book/site. Sears' work on development and infant needs is based in reliable/valid research and human development and well worth review. Sears' The Baby Book (http://astore.amazon.com/peacefparent-20/detail/0316198269) and The Baby Sleep Book (http://astore.amazon.com/peacefparent-20?_encoding=UTF8&node=29) or The Fussy Baby Book (http://astore.amazon.com/peacefparent-20?_encoding=UTF8&node=53) are all excellent and touch on the subjects of cluster feeding and sleep concerns.
At the core, it is normal and natural for babies' sleep patterns to change frequently in the first year of life. Babies each go through their own periods of growth spurts (although these tend to be especially common around 3-4, 6-7, and 9-10 weeks and 3, 6, 9 months). When these times of rapid growth occur, babies will do what they naturally need to do to make more milk --- increase demand! This has to do with the Feedback Inhibitor of Lactation and its impact on mom's milk production: DrMomma.org/2014/08/making-more-milk-breastfeeding-supply.html This is a normal, natural, easy way for babies to control how much/how little they need.
Your little one may also be teething (which can and does happen early for some babies; and teething discomfort often begins 6-8 weeks before a tooth emerges). Some ideas for making life easier for baby when this happens: DrMomma.org/2009/07/teething-pains.html
The foundational solution to all these things? Nurse on cue and allow a baby to snuggle/sleep according to her own perfect timing as well (ditch clock-watching or schedules in babyhood). It can be tough on mom (which is why none of us are meant to mother alone in isolation). Ask a partner to hold/wear/rock baby for 2-3 hours so you can catch up on sleep; or hire someone to help for a couple hours several days a week (just to wear/rock/hold baby) while you nap (or shower or relax). Mothering in community with others, or getting a few hours of help a few times a week has saved many moms in the new months of babyhood. SitterCity.com and Care.com are two great options for finding inexpensive, but good, help with a gentle sitter to hold your baby while you sleep. Asking a relative, neighbor, friend, church-member, etc., are additional options.
Another key solution is learning early in the newborn days to nurse while laying down with your baby. Safe cosleeping (or co-napping!) is how mothers have survived and babies have thrived throughout all of human history, and in most of the world today. Join a breastfeeding group, or cosleeping group, and ask for tips from others who have been there before you. Sleeping while nursing is another life-saver that hugely benefits mothers and their little ones.
Remember, even during the weary, tired-eyes days and nights of early motherhood, this is a brief and fleeting time and will not last forever. It can seem like this is not the case, especially when your baby is nursing every hour, or cannot leave the breast, but these days and nights will quickly become a distant memory of early babyhood.