Disclaimer: I am a visitor here from Electrical Engineering SE. Exceeding recommended safety ratings always comes with some amount of risk. Whether that risk is significant can vary greatly depending on the particular situation. Take the following answer with the greatest of precaution.
I don't think the difference would cause any significant issue, as any hard failure would blow the 3 Amp fuse just as fast as it would a 2.5 Amp fuse, for most practical purposes.
In higher powered or more critical situations, one would be wise to be very careful about safety concerns. In this situation, 3 Amps of current would not likely even come close to pushing the limits of the branch circuit to which the item is connected before the 3 Amp fuse blows.
If the offset in ratings between the two different valued fuses were larger, then there might be some room for concern, but one has to consider that fuses are not an exact science. In their simplest form, their tolerances can vary greatly.
According to the manufacturer "Littelfuse" on page 4 section 1 in this PDF, just a change in temperature alone can change the rating of the fuse by 25%. Furthermore, section 3 on the same page actually shows a situation where a circuit that is intended to blow a fuse at 2.25 Amps, actually should use a 3 Amp fuse.
- NORMAL OPERATING CURRENT: The current rating
of a fuse is typically derated 25% for operation at 25ºC to
avoid nuisance blowing.
In view of this, the 2.5 Amp specification being 16% less than the 3 Amp fuse you would like to use seems insignificant. Based upon the above-linked PDF, the original 2.5 Amp fuse could have passed over 3 Amps of current before it blew if the fuse were very cold.