The weight of ATF fluid will vary by the manufacturer, as there is no set standard weight of ATF fluid.
The most common Automatic Transmission Fluid (ATF) in North America is SAE J1703, which specifies an overall kinematic viscosity range of between 9.3 and 12 centistokes (the unit used to measure viscosity), and limits the variation between cold temperature properties and hot temperature properties. A bottle of transmission oil meeting this standard should have the designation “ATF” somewhere on it so you know you have purchased the correct product. Some other common ATF’s include J300, which specifies a kinematic viscosity range of 10.3 to 16 centistokes, and J306 with the same kinematic viscosity range but requiring specific gravity properties within 0.88 and 0.96 (specific gravity is another measure of weight).
The most accurate way to determine the weight of ATF fluid is to check the bottle or product description, which will usually list the weight somewhere in its specifications.