Why have different pattern altitudes for different aircraft?
Several possible reasons.


Speed differences between aircraft classes. Larger jets cruise and land at much faster speeds than single-engine props. Keeping their pattern separate from slower traffic minimizes problems posed by a faster plane entering the pattern behind a slower one.
Noise abatement. A jet, even a smaller private one at near-idle in approach, is loud. Keeping them higher increases the distance and number of thermal strata to shield nearby residents from traffic noise.
Prevailing instrument conditions and relative pilot experience levels. A ceiling below 1000 feet, the small craft pattern altitude, would ground VFR flights and thus drastically reduce the number of small craft in the first place. Jets, turboprops and other larger planes are much more likely to be IFR-capable (plane and pilot) and so they're placed higher because they can deal with clouds in the pattern (the airport, if towered, would likely alter pattern height to clear cloud layers but traffic holding above the clouds would still require an IFR approach).