Should I upgrade 2x6 attic floor joists by sistering some or all with 2x8s?
I suspect where they are screwed together, they overlap and there's a load bearing wall beneath.  Is that correct?  

You say the span of the joists is "probably 6 feet" but that the critical measurement.  If they're really only 6' long, 2x6's at 16" on center are fine, in fact they'll go a bit further under normal conditions.  

If they are older dimensional lumber, back when a 2x6 was actually 2" by 6", they'll go even further.  

Have you noticed any deflection (bounciness) or sag?