If you're just making the same tool at higher TL, it can be cheaper, lighter, more functional, or all three (an adjustable spanner with a nice plastic grip, or a screwdriver with a magnetic tip, are good examples).
A higher TL tool kit may well not be lighter - because for a moderately comprehensive tool-kit, the amount of stuff you'd be expected to have increases as technology progresses.
Taking mechanical tools as an example: the spanner as a tool is only relevant if nuts and bolts are a thing.
A 'saw' or 'cutter' is an inevitable tool - but you try using a modern (TL8ish) cutting torch on a twisted bulkhead made from TL12 crystaliron that can laugh at a megawatt-range antiship laser and see how far it get you.
The existence of a TL8 powered impact wrench to fit high-torque bolts at manufacture requires a similar level tool to un-fit the things. come TL15 and you're probably looking at trying to unfasten stuff that's micro-welded at an atomic scale.
I've had a little bit of experience of this - in explosive atmospheres (say, oil fumes, or certain bits of a chemical plant), one safety precaution sometimes used is 'non-sparking' tools, which are made from bronze rather than steel. After trying to use bronze cutting and wrenching tools, I can say I honestly understand why we gave up on the metal as a bad idea for general use rather a lot of thousands of years ago....