Varanasi is a spiritual place and it is very closely linked with Indian culture. Wear decent clothing throughout your trip. Modest cloths would avoid awkward stares from locals. Some temples like Kashi Vishwanath Temple has a strict code of wearing saree to enter the temple. Temporary sarees are available in the temple.
During summer, the temperature will be very high and humid. It is advisable to wear light clothing. Cotton is the best material to choose. Since you would be doing a lot of walking around the city, it is better to choose walking shoes or flip-flops. You would be requested to leave your footwear outside the temples and the safety of your footwear is not guaranteed. Thus, do not wear any expensive footwear. Carry a hat or umbrella to protect yourself from sun rays. Sunscreen lotions is also advisable. The summer nights are also considerably hot and thus, you need not worry about packing thick quilts. Light nightwear will be sufficient.
The showers will not be heavy and harsh but there will be continuous showers, which makes the place, slippery. Choose strong gripped shoes and avoid heals. Boots can be preferred. Carry an umbrella or raincoat with you. Thick cotton is enough during daytime. If you are planning to tour during evening, stick to mild wool dresses. A thin jacket over your dress will be sufficient too.
Jackets and warm wear are essential. Winter nights will be very cold and thus, thick jackets and shawls are necessary. If you are planning to take an early morning trip in winter, beware of the foggy climate. Carry Vaseline or moisturizer with you during winter.