Although yes it is overkill it’s probably not stupid overkill. It gives you the option of upgrading to a 1080p monitor and/or it should meet your needs for longer before needing your next upgrade.
The difference between the 3gb and 6gb isn't just the vram but the 6gb has a increased cuda cores which does allow it to perform a bit better. If the budget allows I would recommend the 6gb version.
Given the 1600x900 screen only has 70% of the pixels of a 1920x1080... AND ASSUMING that OP isn't planning to upgrade monitors anytime soon, this makes me wonder if the 1050Ti would actually be sufficient for max details at 1600x900.