Philip R. Bevington, Data Reduction and Error Analysis (McGraw-Hill, 1969), pp. 134ff and 204ff. A classic introduction to least-squares fitting.
Gene H. Golub and James M. Ortega, Scientific Computing and Differential Equations (Academic Press, 1992), pp. 89ff and 139ff. Another good introduction that also discusses using QR factorization.
Matthew Lybanon, Amer. Jour. Physics 51, (1984), p. 22. Discusses a modified and improved effective variance technique.
Jay Orear, Amer. Jour. Physics 50, (1982) p 912. Introduces the effective variance technique.
William H. Press, Brian P. Flannery, Saul A. Teukolsky and William T. Vetterling, Numerical Recipes in C (Cambridge Univ., 1988), Chapter 14. The code of the LinearFit package largely uses the notation of this book, which also discusses singular value decomposition.
William H. Press and Saul. A. Teukolsky, Computers in Physics 6, (1992) p. 274. A discussion of fitting when the data has errors in both coordinates, with an example of the Brent method.
J.R. Taylor, An Introduction to Error Analysis (University Science Books, 1982), p. 158ff. A good discussion of least-squares techniques, this also discusses the "statistical assumption" used by LinearFit when the data has no errors and the Reweight option is set to True.