In geophysics the rotation-of-Earth-effect that you are describing is called the Eötvös effect.
The wikipedia article was initiated by me (and has remained largely unchanged since.)
In geophysics the expression 'Coriolis effect' is by convention used for rotation-of-Earth-effect for motion component parallel to the local surface. That is: in geophysics by convention Coriolis effect on motion is treated as if the objects in motion are confined to moving parallel to the local surface.
In geophysics distinction between Coriolis effect and Eötvös effect is by convention; the underlying physics is the same.
The following is copied from the wikipedia article (that I wrote)
The most common design for a gravimeter for field work is a spring-based design; a spring that suspends an internal weight. The suspending force provided by the spring counteracts the gravitational force. A well-manufactured spring has the property that the amount of force that the spring exerts is proportional to the extension of the spring from its equilibrium position (Hooke's law). The stronger the effective gravity at a particular location, the more the spring is extended.
For the calculations it will be assumed that the internal weight has a mass of ten kilograms (10 kg; 10,000 g). It will be assumed that for surveying a method of transportation is used that gives good speed while moving very smoothly: an airship. Let the cruising velocity of the airship be 25 metres per second (90 km/h; 56 mph).
To calculate what it takes for the internal weight of a gravimeter to be neutrally suspended when it is stationary with respect to the Earth, the Earth's rotation must be taken into account. At the equator, the velocity of Earth's surface is about 465 metres per second (1,674 km/h; 1,040 mph). The amount of centripetal force required to cause an object to move along a circular path with a radius of 6378 kilometres (the Earth's equatorial radius), at 465 m/s, is about 0.034 newtons per kilogram of mass. For a 10,000-gram internal weight, that amounts to about 0.34 newtons. The amount of suspension force required is the mass of the internal weight (multiplied by the acceleration of gravity) minus those 0.34 newtons. In other words: any object co-rotating with the Earth at the equator has its measured weight reduced by 0.34 percent, as a consequence of the Earth's rotation.
When cruising at 25 m/s due east, the total velocity becomes 465 + 25 = 490 m/s, which requires a centripetal force of about 0.375 newtons. Cruising at 25 m/s due West the total velocity is 465 - 25 = 440 m/s, requiring about 0.305 newtons. This gives a difference of about 0.07 Newtons (0.375 - 0.305).
So if the internal weight is neutrally suspended while cruising due east, it will not be neutrally suspended anymore after a U-turn. After the U-turn, the weight of the 10,000 gram internal weight has increased by about 7 grams; the spring of the gravimeter must extend some more to accommodate the larger weight. On the other hand: on a non-rotating planet, making the same U-turn would not result in a change of gravimetric reading.