Recommended readings (for students)

WEAVER++ has been developed within the general framework of the theory for speaking advanced by Pim Levelt in his book "Speaking: From intention to articulation" (1989).
The combination of a symbolic network and production rule system with spreading activation and activation-based rule triggering was originally proposed for ACT in "The architecture of cognition" by John Anderson. There have been many new developments within the ACT framework, but the 1983 book is still a recommendable read.
Much of the mathematics (e.g., hazard rate functions and probability densities) behind WEAVER++ can be found in the classic "Response times: Their role in inferring elementary mental organization" (1986) by Duncan Luce.
An early introduction to functional brain imaging and electrophysiological techniques can be found in "Images of mind" (1994) by two pioneers of the field, Michael Posner and Marcus Raichle.
An explanation of "physical symbol systems" and the general philosophy behind computational modeling can be found in "The sciences of the artificial" by Herbert Simon. Read the third, expanded edition of the book, which appeared in 1986.
An interesting evolutionary account of the role of language in shaping the human brain and vice versa (an alternative to the views of humans as chimpanzees-with-grammar or genius-chimpanzees) is given by Terrence Deacon in his "The symbolic species: The co-evolution of language and the brain" (1997).