One of the reasons why small cogs are noisier is that they are not truly round. This is also true with larger cogs but the effect is less. 11 tooth cogs are particularly bad in this respect. Another reason small cogs are noisier is that there are fewer teeth engaged with the chain so each cog carries a bigger load. Even with minimal chain stretch, when the chain disengages from the last cog as you pedal there will be some noise. If you use the smallest cog frequently, it will wear much faster than a bigger one, and if you hardly ever use it, it will be much less worn than the others that you use all the time. Depending on how you ride, certain cogs in all cassettes wear faster than others which is why when you install a new chain and notice that it slips it will only be in one or two gears