SQL Server 2008: Unused Clustered Index
But you have an index on TweetID.  Is that index not used by the joins?  

Even a non-clustered index will fragment with insert and update.  As that index fragments inserts take longer.  How are you managing fill factor and index maintenance on this non-clustered index?

An unused PK does nothing.  

TweetID as PK will save some space.  What % of rows get added daily.  If only 1% rows get added daily you could use a fill factor of 90% and defrag daily or weekly.  Start with like 80% or 90% and see how fast it fragments.

If the TweetID are out of order but in the same range then the problem you have there is fill factor gets hammered in that range and unused in the rest of the range.  But a defag is faster as it is only cleaning up that part of the range.  In that case you may be better off with 100% fill factor and a regular index reorganize.

There is no cut and dry answer.  You need to manage and monitor the index for your data and your workload.