Let me preface with I am completely new to gardening and live in a townhouse so I have to use containers. Lots of the leaves of black dots on the underside, or get brown and rotten while other leaves are OK.
Too far away to see details.
Sweet basil is too disease prone. In contrast Asina basils (Thai, cinnamone) are tough. I have several kinds. Sweet basils are all sick but the others are doing just fine.
No more sweet basils for me next year.
Can't tell much from the photo, but it sounds like downy mildew. It spreads extremely easily, and thrives in humid conditions. I had it wipe out 8 sweet basil plants, it eventually infected my thai, cinnamon, and purple basils. I had limited success pruning any leaves showing any sign of infection, and keeping them as separate as possible. A few heat waves helped minimize it popping up on leaves again, but it's tough if not impossible to get rid of short of starting containers over.
Here is a link that might be useful: Cornell University Warning of Downy Mildew