LOL! You can take out the cat, but it's still a dog!
My notes from when I swapped the exhaust on my Bonneville was that I knocked off under 7 lb. 7 lb with a 10 hp improvement to boot is nothing to sneeze at. For weight reduction, I also swapped on an alloy handlebar, swapped the rear shocks, removed the carbon canister and the air injection and every other thing I could find that didn't offer any measurable value in reliability or function, for probably for another 5-10 lb total weight reduction on the Bonnie. So that's a total weight loss without making functional changes of about 15-20 lb. My Scrambler is in similar condition, still a work in progress.
I'm sure with a similar kind of approach you could knock 15-20 lb off of one of those Triumph 400s. But getting more than 20 lb weight reduction is going to be difficult, expensive, and most likely involve functional changes you probably don't like, such as removing, or often cutting off, parts you actually would like to keep on there because they're useful.
Triumphs are expensive bikes to work on. Parts and accessories are all among the most expensive on the market. You can take off unnecessary stuff and maybe save 5 lb without paying a cent for it. But other than that, my math says it'll likely cost you about $100 for every lb you want to remove. Maybe your $600 aftermarket exhaust that reduces 6 lb is worth it since it comes with a performance increase above just the weight, and looks better. But after that, it starts to feel pretty expensive, especially on a brand new motorcycle that cost under $8K to start. If you don't mind voiding the warranty and venting fuel vapor into the air then 15 lb is probably on tap for the cost of the new exhaust. Then after that another 20-30 lb might be available at $100/lb. and some loss of function. Removing more than 45 lb total is going to require intense surgery, like fabricating a whole new chassis from aluminum or swapping the wheels for some handcrafted forged alloy track wheels that'll bend if you give them a harsh look.
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