Pointless to save the weight really, mainly due to the 6.8kg uci rule still being involved (if you race). Also there is no advantage to cutting the weight as you rarely have to increase the pace from standstill IMO.

However I'm not thinking I will weight my track bike!!

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it depends on your events. if you do sprints or any standing starts, imho stick with 1/8. if you are just a pursuiter, then by all means go 3/32 and lighten all the other rotating parts while you're at it.

BTW Izumi chains and some other brands stretch very fast, even the 1/8". Track riders often are on a stretched chain without realizing it. At 3 o'clock on the front chainring, pull the chain away from the chainring. you'd be surprised at the gap.