There are all kinds of different adversary models: these kinds of algorithms are tailored towards IoT or short-term communications use cases, where size and performance on constrained devices are more important than being secure against a nation state for X years.

For example: you may have a “smart” device in your household that indicates whether you’re home or not. You don’t want a passive adversary to be able to snoop its RF traffic, but you also don’t need its traffic to be secure for more than one week. “Lightweight” algorithms are meant to give you formal guarantees around that, while also balancing performance, power consumption, and other interests.

More like "lightweight" in terms of code size (or hardware equivalents like FPGA fabric area), RAM requirements, and CPU cycles per byte of encryption/authentication. In some cases this means that a message could be brute forced slightly more quickly. But in practical terms that not a big deal, who cares if someone can crack your code in 2^10 years instead of 2^14.

I think for most crypto, brute force times aren't the biggest concern. What's more potentially an issue is the breakability of the algorithm (is there a way to find the plaintext more efficiently than brute forcing?) and how susceptible the algo's implementations are to things like timing attacks (which can be an issue with s boxes although maybe not as big of a deal as I thought considering the results of the competition).

In terms of NSA conspiracy theories, it would've been more of an issue if the competition had gone towards Simon or Speck (which weren't eligible because they're block ciphers, but there's ways to adapt... I think OCB mode is no longer patent encumbered.

No, more tuned for small message sizes, code size, RAM usage, power usage, etc. The security goals are essentially the same as the "high performance" ciphers, but the performance trade-offs are different.

No. Size of algorithm is unrelated to security.

add "at scale" (= IoT edge devices)?