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You can have a half-arsed go with: https://fellrnr.com/wiki/Running_Calculator
If I put in my "best" 5k time of 24:24 at 83kg I can see that it suggests (Weight Adjusted Race Times) that at 78kg I could get to 23:10.
Note: This is assuming you're losing fat, if you're already skinny then it's not going to automatically make you faster.
(You can then enter that time/weight and see what it says for further losses, although you're really compounding the guesswork at this point.)
The whole https://fellrnr.com/wiki/Weight_Loss_and_Performance section is worth reading though.
Greenbank-
I can send anyone a working spreadsheet that this is based off (based on a bunch of tables put together by Daniels, J. and Gilbert, J. (1979) Oxygen Power: Performance Tables for Distance Runners., if'n you're interested).
Side note, I did have a bit of work going on where I was going to update the whole VDOT schtick with a few hundred million activity records (compared to the Daniels & Gilbert not-many-activities-at-all), but strava stopped all access to their data.
It's still a very useful s/s though, showing race pace prediction, training pace targets, and variations due to weight and temperature.
NotThamesWater
Yes very much this! I was wondering the other day how much difference it would make if I lost say 5kg in a controlled manner. I reckon my knees would be chuffed if nothing else