Let's give this a try.

Claim: Relying on few strong arguments is more reliable than relying on many weak arguments.

• Motivated reasoning is a bigger risk when dealing with weak arguments, since it is relatively easy to come up with weak arguments on the side that you favor, but it is hard to make an argument rigorous just because you want it to be true. It also seems easier to ignore various weak arguments on the other side (or dismiss them as not even worth considering) than to dismiss a strong argument on the other side.
• Selection effects will tend to expose you to more weak arguments on one side of an issue; e.g. if you are surrounded by Blues then you will be exposed to lots of weak arguments in favor of Blue positions, and few arguments in favor of Green positions. A person in this Blue-slanted situation has a better chance of finding their way into the pro-Green camp on an issue if they ignore the argument count and instead only compare the strongest pro-Blue argument that they have seen with the strongest pro-Green argument that they have seen (or, even better, the steel-manned version).
• The 80/20 rule: in many domains, a small fraction of the things carry a large portion of the weight, and a useful heuristic is to focus on that small fraction (e.g., the 20% of effort that produces 80% of the results). Which suggests that, in this domain, the strongest few arguments will carry most of the evidential weight on an issue, and the long tail of weak arguments will not matter much.
• Nonindependence: a set of arguments on a given issue are rarely independent; arguments which share a conclusion often have strong (and perhaps hidden) dependencies and interrelationships. For example, a large fraction of the set of arguments may all rely on the same methodology, or come from the same group of people, or be (perhaps indirect) consequences of a single piece of evidence, or share a single auxiliary assumption. So a set of seemingly independent arguments often provides less evidence than it appears.
• Argument structure: the structure of a complex argument is often important but neglected, and it is not accounted for by listing simple points in favor of each side. To take one example, the claim IF (A or B or C or D or E) THEN Z has a very different structure from the claim IFF (A & B & C & D & E) THEN Z, but moderate evidence against D would appear similarly as "a weak argument against the claim" in both cases. Making a strong argument requires engaging with the structure of the argument.

I can already see some counters to these arguments (and some counters to those counters), but I suspect it would be more useful to have a list of arguments on the other side in the same format to compare these with.