I find this direction really interesting, but I also agree with the concerns mentioned above: as long as weight can be exchanged for visibility, someone will inevitably find ways to game it.
My own approach would be more conservative: instead of directly tying weight to permissions, treat it as a reference signal. For example, pilot it on a small scale to see which interactions are sustained and cross-topic, rather than focusing solely on one-off votes on individual posts. Single votes can easily be amplified by cliques, whereas interactions over time are much harder to fake.
Another question I’d like to ask: if a new member starts with little weight, will their thoughtful replies actually be less likely to be seen? How would you avoid this “chicken-and-egg” problem?