Exactly
The RS and the Type R are the lightest shells, i wold take a Type R for the racing pedigree, while keepig it stock. The RS would be a track car, lightest base=the fastest. I believe the GSR is the heaviest as i think the motor weights slightly more and the GSR has all the optional extras that the LS didnt have standard ie wing etc.
But the weight difference is still not THAT much different.
DC 1994 Acura Integra GS-R Coupe MT 2667
DC 1994 Acura Integra LS Coupe MT 2643
DC 1994 Acura Integra RS Coupe MT 2529
DC 1998 Acura Integra Type-R MT 2577
1993 Honda Civic VX HB MT 2094<--thats light
A carbon fiber hatch/hood and stripped out interior in an LS or GSR would bring you pretty dam close to the weight of a RS. Do you really think you will feel that extra 138lbs of difference between a GSR and a RS? (I'm being serious here not a smart ass) You'd be much better off buying a 93 Civic VX and throwing a H series or something in it.