The tube system of aerospace vehicles is a functional system formed by ducts, fittings, and hose clamps, etc. which are connected in series or parallel and fixed to the structure. Due to factors such as the accumulation of manufacturing and positioning errors of components, assembly deformation, and weak support stiffness, there exists a significant deviation between the actual assembly posture and the theoretical state. The assembly deviation of a weak-stiffness tube system exhibits characteristics of multi-source and non-linear coupling, making it difficult to conduct quantitative analysis of the assembly deviation of the tube system through methods such as dimensional chain or error modeling. Traditional rigid, specialized positioning fixtures are heavy, have long manufacturing cycles, and are unable to meet the positioning requirements for assembly of weak-stiffness tube systems. In response to the aforementioned issues, this paper summarizes and outlines the characteristics of the assembly deviation in tube systems of aerospace vehicles. We have established a multi-source, nonlinear error transmission and coupling model for weak-stiffness tube systems. A method for the assembly positioning and deviation analysis of weak-stiffness tube systems based on laser projection has been proposed. Calculations and simulations of laser projection positioning under various assembly deviation conditions have been carried out. We have developed a flexible, compact, and modular assembly positioning and deviation analysis device for weakly stiffened tube of aerospace vehicles. Through experimental validation, it has been confirmed that this method and device hold significant engineering application value. They are suitable for the assembly positioning of weak-stiffness components under discrete manufacturing conditions.