If you want to reduce weight, there are couple of "free" things you can do. However, note that everything you do is a sacrifice for luxury and comfort.
Stage 1
Spare Wheel - Replace this with a fix a can instead, this will free up a fair bit of weight in the rear. However not significant enough to feel an acceleration difference, handling may slightly improve depending how well you already know your car to feel the difference.
Rear Seats - This is also heavy, and also the easiest reverse if need be. If you don't have a tenancy to carry passengers, remove this and it'll further reduce more weight. When this is removed, you will start hearing more cabin noise especially from the engine and exhaust.
Stage 2
Panel Trims & Carpetry - Depending on how extreme you take it, I don't believe TSX owners will go so far. Removing this will almost remove all sound insulation as well while saving weight. A harder process to reverse and most definitely not necessary.
Tar / Permanant Insulation - Dry ice is your friend if you want to take it to the extreme and remove all the black bits and pieces Honda put in place to reduce road noise and contact from the road. This is not reversible and will expose the full core metal of the chassis.
Stage 3
Body Panels - Unfortunately there is not much development on this even in Japan, in search of a dry carbon bonnet/boot lid will remove enough weight to improve acceleration and handling. However, this is when it starts getting expensive. Dry carbon reduces weight, not wet carbon.
Bucket Seats - Factory seats are very heavy, especially those ones with plenty of comfort and padding along with electronics and memory. Replace them with full one piece bucket seats will see significant weight reduction as well.
Chassis Reinforcement - Rollcage custom fabrication, for all the weight removed, the chassis now needs to be strengthened. This will no doubt be permanantly and illegal in some states and countries for public road use.
So, as you can see. You can take it from S1 to S2 and to S3. How extreme you want to take it would be a bigger question. I don't believe the majority of TSX owners will take it pass S1.