I have the Backcountry.com 700 ml ti pot (which is just under the 3 cup capacity you listed). I removed the handles and ditched the lid on the pot and then supplemented it with an aluminum baking sheet lid. The total weight is 2.7 oz for the pot and lid.
Backcountry does not sell the "Backcountry" pots anymore, but they do sell them branded as "Stoic", however, I am curious if the titanium on the Stoic pots are a bit thicker than that of the older Backcountry pots... So, I can't say what that weight would be. However, these pots are on sale for less than $20 often...