Déjà vu is not simply a weak memory, but rather from a separate memory system in our brains. Perirhinal cortex creates familiarity while hippocampus handles the detail.
Paper: Episodic memory, amnesia, and the hippocampal–anterior thalamic axis
Scientists used to think our memories were simply strong or weak, like points on a line. There, the feeling of déjà vu, that peculiar sense of familiarity, was often explained as a "weak" memory with the assumption that our memories fall along a continuum. However, in the late 1990s, researchers Mishkin, Aggleton, and Brown discovered that memory actually has different subcomponents, and each can be either strong or weak.
Among these subcomponents, the perirhinal cortex supports familiarity-based recognition (knowing), while the hippocampus supports recollective-based recognition (remembering).
For example, perirhinal cortex is like seeing someone and thinking "I know that face" even if you can't recall anything else about them. On the other hand, hippocampus helps you remember exactly where and when you met them, and what happened during that meeting.
Research on people with damaged hippocampus shows this difference clearly. These people can still feel that things are familiar, even though they can't remember specific details about their experiences. And even without specific recall, this sense of familiarity can be so strong that it leads to a sense of certainty. They might be absolutely certain they've seen something before, but this familiarity does not provide access to the "where" and "when" of that event because of their damaged hippocampus.
In essence, déjà vu is not a weaker form of memory, but rather a different type of memory altogether. So when you feel the sense of familiarity but don't remember the details, the perirhinal cortex in your brain is activated without using the hippocampus to gather the temporal and spatial context.