The low speed fuel circuit in the carburetor is clogged from old fuel varnish. The carb will need to come off, completely disassembled, soaked in a commercial grade of carburetor cleaner overnight, rinsed and blown dry then all of the fuel passages and jets checked for flow before being reassembled. Honda has reduced the price on their carburetors to where in many cases it is more cost effective to replace the carburator rather than trying to rebuild it.
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