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Acceleration due to gravity will increase.

As the Earth is rotating about itself, all objects and people are going around in a circle every day.  In order to move in a circle like that there is a force required.  Thus some part of the gravitational force makes us go around in that circle.  The remaining force is equal to the apparent or observed weight of an object on the surface of earth.   So apparent weight is less than true weight.

If Earth is not rotating about itself,  then all the gravitational force of attraction is equal to the weight.  Hence the apparent weight is same as true weight.

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value of g = G Me / Re^2 remains same. But acceleration due to gravity increases. now when earth rotates effective g' = g - Re w^2 = (g - 0.034) m/sec^2. When earth stops rotating, g' = g.
If the earth stops rotating then the value of 'g'at equator will increase because when the earth rotates the gravity at every point remains uniform and when it stops rotating, the gravity increases as pressure is exerted on only one point at the equator.