As a former (freelance) software engineer, I consider the source code (or, in this case, the project files) to be worth, at least, ten times the finished program (or video file). Therefore, if the finished video file is worth $5000, your project files are worth $50000 plus.
Like a software engineers source code, your AE project files are your intellectual property. Just because you’ve used well known techniques and expressions, makes no difference, whatsoever. Software engineering is (basically) all about the creative use of common techniques and blocks of standard code. As you can see, the software/source code analogy is exactly the situation you have asked about.
If I were you, I’d offer the project files, with an appropriate price tag. If your clients client is unwilling to pay your price, they don’t have any right to expect to be provided with any project files.
Of course, I am assuming that you have provided them with everything that you were contracted to produce for your client, i.e. you were contracted to produce and deliver a finished video file (or a motion graphics package, or whatever), but not an After Effects template/project files.