In general batching is the process of measuring and combining the ingredients of concrete (cement, water, sand, aggregates)…as per the mix design. The last part is important, if you are an Engineer then you will have to do a concrete mix design to know the quantity required for each element of concrete…so basically, you will say “for C-30 concrete member we need 50kg of cement per meter cube of the member or 20kg of aggregate per meter cube…etc this is the mix design. Now the batching( measuring and mixing) could be done in two ways like you said. Weight batching is the professional one, which is always recommended. Basically, you measure each quantity by mass (using a large weigh equipment) and batch the components in a controlled environment.
The choice of batching method depends upon size of job, production rate and standards of batching performance.
Traditionally batching is done by volume. Batching accuracy is important. It is however recommended to do weigh batching rather than volume batching. Volume batching may be allowed only where weigh batching is not practical.

The figure below shows the difference between weight batching and volume batching of concrete

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