Sweet basil is an annual. That means it generally lives for one growing season. Some people can keep them going for longer but they are definitely not as robust once you go beyond that one season.

Sweet basil also enjoys heat and full sun. For me, it wants all the heat and sun it can get. But I do not know how much heat basil can withstand - I live in a place that can have freezing temperatures for half the year. Someone from a warmer place than I will have to comment on that.

But you will need to give your plant more light to keep it healthy. The conditions you are describing doesn't provide enough light. Some extra lighting meant for growing plants may help or if you have a balcony, give it some real sunlight.

FataMorgana

I have had very limited luck with growing basil in a pot, probably due to insufficient light. I have a couple good east windows but the basil still gets long and leggy. I save my windows for overwintering plants that will be happy under my indoor conditions and harvest lots of basil during the growing season to use over the winter. I both freeze both whole leaves and leaves pureed in olive oil.

It looks like Basil is not going to be too happy unassisted where I'm growing it. It's also raining here so the sun is even less. I think I'll look into adding artificial lighting to help it grow. Thanks for your inputs!