You could measure weight with a spring scale, unless you mean mass, which you would measure with a laboratory balance. You would measure time with a stop watch, and height with a meter stick.
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Weight: a spring balance.Time: a chronometer
Height: a tape measure.
However, in all cases, these would not be appropriate in all cases. You could not use a spring balance to measure the weight of an elephant, or a tape measure for a mountain.
The metric unit commonly used to measure height is the meter. So, you would measure the height of Big Ben in meters.
You would use the metric unit of meters to measure the height of a gallon of milk.
You would most likely use milliters.
You would use the metric unit "kilograms" to measure the weight of a bag of groceries.
You would use the metric unit "kilograms" to measure the weight of a sack of peaches.