I don't think "Harrison Bergeron" has any one correct interpretation. It is a satire of the basic human emotion of jealousy, first and foremost. Any political interpretation is secondary, and debatable.

If you are left-wing, you can see the shackles, weights, etc. as a metaphor for money / inherited privilege. There are many talented people in the world who never get to make use of those talents because financial difficulties (weights) hold them back. "Capitalism does not let beautiful things flourish," is the message.

If you are right-wing, you can obviously see the shackles, weights, etc. as literal. The government is some wacko communist government that actually puts shackles on people to make them all "equal." The message is that "Communism would make people miserable by not letting individuals reach their full potential." (I don't think that was Vonnegut's intended message. Karl Marx's whole philosophy is about letting individuals flourish. Harrison Bergeron and his parents and the ballerina are all VERY alienated from themselves and their labor.)

But really, it's just a fun sci-fi short story about a dystopian, authoritarian government that does not seem to have a real-world ideology except cartoonish evil. The point, at the end, is that Harrison's mother doesn't even remember seeing her son do all that stuff on television, because her and her husband's attention span has been destroyed by technology. The point is that in the future, individual expression will be lost in the haze of technology, alienation, and an oppressive world that moves too fast. That could also be a summary for "Capitalist Realism" or any Adam Curtis documentary.