I learned recently about Koorathaazhvar and Kulothunga Chola's apparent argument, although I'm not interested in the context it was used, I'm curious about the question, as what and when are these meters(drona, shiva)used, and what other such meters are there?
The measurements Drona appear in many ancient texts. Dronacharya, who is the teacher of Kauravas and Pandavas was named after a bucket or a wooden vessel.
When Krimikanta Chola asks to sign a document saying there is no one higher than Shiva, Kurathalzhwan adds a line but Drona is higher. Here, Koorathazhwan was meaning the measurements.
There are certain measurements given in an ancient Ayurveda texts named Ṣoḍaśāṅgahṛdayam. From wisdomlib.org
Guñjā (Raktikā) = 1 seed of Guñjā
8 Raktikā = 1 Māṣa (1 gram)
10 Māṣa = 1 Karṣa (10 grams)
2 Karṣa = 1 Śukti (20 grams)
2 Śukti = 1 Pala (40 grams)
2 Pala = 1 Prasṛta (80 grams)
2 Prasṛta = 1 Kuḍava (Añjali) (160 grams)
2 Kuḍava = 1 Śarāva (320 grams)
2 Śarāva = 1 Prastha (640 grams)
4 Prastha = 1 Āḍhaka (Pātra) (2.56 kilograms)
4 Āḍhaka = 1 Droṇa (10.24 kilograms)
4 Droṇa = 1 Droṇī (40.96 kilograms)
100 Pala = 1 Tulā (4 kilograms).
When it comes to measurement named Shiva, it is lot smaller than Drona. It corresponds to a measurement of a peg. Monier Williams Dictionary gives one of the many definitions. The related one to measurements is
a peg, L. [ID=217521]
But I couldn't find exactly in which text this measurement is given.