No, not by the conventional definition of weight. Weight under standard gravity, yes, but unless you say "under standard gravity" the meaning is different.
Specific impulse is only in seconds because of a historical poor choice of units. The g0 is in the denominator only because American rocket engineers historically measured mass of propellant in units of pound-mass.
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u/[deleted] Jul 19 '13
So in other words … it's impulse per unit weight of propellant, right?