When I run your example, RSS jumps from 20 MB to about 1,600 MB. There is almost no increase when I run the look several more times.

>>> p.memory_info()
pmem(rss=19902464, vms=240513024, shared=10014720, text=2125824, lib=0, data=9887744, dirty=0)
>>> asyncio.run(main(2000))
<stdin>:2: DeprecationWarning: The explicit passing of coroutine objects to asyncio.wait() is deprecated since Python 3.8, and scheduled for removal in Python 3.11.
>>> p.memory_info()
pmem(rss=1608568832, vms=1829105664, shared=10014720, text=2125824, lib=0, data=1598480384, dirty=0)
>>> asyncio.run(main(2000))
>>> p.memory_info()
pmem(rss=1608835072, vms=1829367808, shared=10014720, text=2125824, lib=0, data=1598742528, dirty=0)
>>> asyncio.run(main(2000))
>>> p.memory_info()
pmem(rss=1608601600, vms=1829367808, shared=10014720, text=2125824, lib=0, data=1598742528, dirty=0)


Why are you creating so many SSLContext objects any way? It's very inefficient and really not necessary. I recommend that you create one context in your application and reuse for all connection. You only ever need additional contexts for different configuration (protocol, verification, trust anchors, ...).