Another vote for Baggelini. They are all nylon so very lightweight, come in lots of style and colors, and wear like iron. Reasonable prices. Kipling is a similar brand. I look for very lightweight bags for travel, in part due to a back muscle injury last year, but also just because.
I have a small collection of these two brands, and use them all. The black cross body bag (first find) is the most versatile, being big enough to hold daily needs plus a few extras. I love it for winter city travel (I've been to a few European cities for Christmas) where I need a knit hat and gloves outdoors but take them off indoors and this bag is big enough to hold them so I don't lose them. It also was perfect in Barcelona one summer (supposedly another pickpocket haven) where I zipped it shut , wore it cross body and put my hand/arm over it, and felt very secure.
I'll mention two that don't meet your needs but give an example of how versatile these brands can be. 1) I just bought the gold small one (second find) which was perfect for holding wallet, passport, iphone, chapstick, meds that I wanted easy access to while on long flights with several connections. It stows easily into a larger bag. 2) I also have a Kipling backpack (I think it's sold as a "school book pack" for teenagers) that is the lightest backpack I've ever found, yet has room for my laptop.
If you are a fan of TJmaxx you can usually find both of these brands there, although the styles/colors will be hit or miss of course. Zappos carries wide selections of both, and Macys carries Kipling and a limited number of Baggelinis. There are probably other retailers that sell them too but those are the ones that come to mind for me.