1/4" = not a happy weeder, 1/8" = not going to bother at all. I won't even cut stuff that tiny for myself, much less for someone else
That being said - the more precise the cuts, the easier to weed - provided you don't go blind in the process.
you are reaching the limit of almost all cutters at 1/8" - there just isn't enough adhesive left trying to grip the slippery paper it is mounted on. for 1/8" everything has to be perfect - you might try cleaning your place and end of the holder with some alcohol to see if that helps but you are reaching the limits of cut vinyl that small