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There's so many possibilities here. It could be a lack of stability in your setup, a specific muscular weakness or just that you're using heavy weights. Even top lifters shake a little for their big big benches. Personally, I don't think you need to decrease the weight unless you think the shaking might create an injury risk.
There's a lot of potential technique things you can't really ascertain through a forum but one possible quick fix is to make sure that you are squeezing the bar as tight as you can from the moment you touch the bar to the end of the set. Absolute deathgrip. That'll help create tension throughout your entire arm, provide some stability and just make your bench better. If that doesn't help at all then start to look into shoulder position, 'leg drive' to create stability, building weaker shoulder muscles, etc...
Really not getting on with bench press, arms shake but it never feels like I will fail, should I drop weight?