Kimoni Techni is 0.8mm, but still weighs around 18g in my experience. Should bring the size down by about 1.
Various full size ones are around 1.4mm and weigh about 24g. You wouldn't need a special thick one, just a normal one, to align the two. And you can tailor using electrical tape under the grip if necessary, which is around 0.3mm thick and 4g-5g for a single wrap.