Does a character with Arcane Background (Weird Science) need many knowledge skills to go with the Arcane Background? Looking at pregens online I see that some have chemistry, physics or just science in general.
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In the core rules, the requirements for the Arcane Background (Weird Science) Edge is simply "Novice". Since a character is always Novice or higher rank, that means that any character can take the Edge regardless of anything else on the character sheet including a complete absence of Knowledge skills or a bunch of completely unrelated Knowledge skills, like Knowledge (RPG Stack Exchange).
However, there are two Edges in the core rules that are specifically intended to enhance the abilities of someone with Arcane Background (Weird Science). They are:
Both of these Edges include the requirement "at least two other scientific Knowledge skills at d6+", which would include skills like Knowledge (Chemistry), Knowledge (Engineering), and so forth. The only time that a character with Arcane Background (Weird Science) would need to have these skills would be if they were also taking one or both of these Edges in order to create a "super mad scientist." Of course, Knowledge skills can be purchased by anyone just for storytelling reasons, so sometimes characters will have scientific Knowledge skills just because it fits the concept.
Also, there isn't a list of applicable scientific Knowledge skills; the player is just expected to make one up and have the GM agree that it falls under the category of being "scientific". Most GMs will rule that "Knowledge (Science)" is too broad and encourage players to be more specific. I usually see people choose skills from the natural sciences (e.g. Chemistry, Engineering, Physics, Biology) because it fits well with the idea of a mad scientist tinkering with stuff or undertaking experiments. However, I imagine you could also use scientific skills from other fields, like the social sciences. Knowledge (Psychology) might be good for a weird scientist who is interested in understanding how people work and uses powers like Fear and Puppet.
So to succinctly answer your question: no, a character does not need any knowledge skills to go with Arcane Background (Weird Science)? However, if you want to use either of the two core Edges that improve upon it, you will need at least two scientific Knowledge skills. The pregens you've seen with these skills have them either because they have one or both of these Edges or because the creator thought they fit the concept.
The answer is no but ...
To create a Weird Science Gizmo and to use it you don't need any science knowledges but to get the Edge Gadgeteer which allows you to make quick hack to temporarily create a jury-rigged device you do need two science knowledge skills.