Let's aim for some at an introductory level, some articles and some textbooks. Applied is more helpful, including R code is great. Thanks!
Lucky for me, Andrew Gelman decided to discuss this topic on his blog last week! There I found the following books recommended in the comments:
Applied Survey Data Analysis by Heeringa, West & Burglund
Sampling: Design and Analysis by Sharon Lohr
Survey Methodology by Groves, et. al.
Struggles with Survey Weighting and Regression Modeling by Andrew Gelman
The most authoritative reference is Valliant, Dever and Kreuter (2013). Practical Tools for Designing and Weighting Survey Samples, and the accompanying
C.f. other answers so far in this thread, the authors are actual practitioners in the survey field, and producing/weighting survey samples is one of the central parts of at least Jill Dever's job. (Rick Valliant had just retired as of 2017, and Frauke Kreuter runs two graduate programs on two different continents at the moment; all three are highly regarded statisticians in the survey world).
My own little piece concerns some terminology in the survey weighting literature: Kolenikov (2016). Is it post-stratification or nonresponse adjustment? -- see also references therein.