My balcony gets no sun, but the petunias (in a planter) thrived for two months. Now the blooms are sparser, and both they and the tendrils are droopy. Am I overwatering, or are they finally succumbing to the lack of sun? It was a gorgeous plant. I do not know the cultivar.

Can you post a picture? Petunias get straggly later in the season, I'm assuming that's what you mean by tendrils, long stems hanging down? Petunias don't actually have tendrils. When they get to the straggly stage you can cut them back which should rejuvenate them. Check also for aphids because they can contribute to the problem. A picture would help ensure we're on the right track.

Mine did that too and it turns out they were just seeding. A week later and they came back. Check for seed pods.