I found this question very interesting and I will try to answer it. I think it is very hard to answer in current form, as there were so many protests in so many contexts.
Disclaimer: I will concentrate more on the actual outcome, rather than public sympathy evaluation. Clearly, public sympathy is much harder to evaluate than the political, economical or social changes due to a protest, as history concentrates on these more.
In some contexts what is the reference population? That of the cities the protests are located into. The whole country? Also, some protests happen outside of the target country (sympathy protests).
Measuring the sympathy is much easier through the use of technology (e.g. online polls), so it is much harder to evaluate for some past events.
I do not think there is a correlation between protest size alone and public sympathy, even less the outcome of that protest. The context of a protest can be very complex and determine both the sympathy and the outcome:
- global political context
- local political regime
- economical context
- social context
- cultural context
- protest technique
I will choose some notorious protests mostly in the European World to illustrate this conclusion. Why European? Because it had an interesting (not necessarily in
a good way) in the past 120 years, with lot of changes: severely affected by both WWs, the Iron Curtain, developing countries, UE and NATO extensions.
This include some protests, their estimated size, public sympathy evaluation and the outcome.
Estimated protest size 3000 and it happened outside of India. According to this source the protest was repressed, but many sympathized with the protesters and the government had to negotiate with them. But more important, Satyagraha (non-violent resistance) was born.
Protest size was rather small, but protest technique (non-violent) helped gaining sympathy and forcing authorities to negotiate. Cultural background is also important, as those people were prepared to endure lot of suffering to obtain what they wanted (this is visible later, when India non-aggressively fights against the British occupation).
- 23 October 1956, Hungarian Revolution - 20000 protesters gathered in Budapest (out of about 10M population of Hungary back then => 0.2%). I assume large public sympathy in Hungary. The Government fell, but the Soviets intervened military and restored the political regime.
The political context was against this uprising: see Suez Crisis and Cold War. Also, Soviet Union was already known by the harsh policy against those opposing the mainstream policy. See Stalinism, forced settlements, Gulag.
- 5 January 1968, Prague Spring begins, the soviets eventually Czechoslovakia and non-violent protests occur against the invasion. I could not find information about the local protest size (thousands or tens of thousands max), but the public sympathy was very large: Romania, Italy, France,
Finland and many others, including Russia.
Again, the political context was against the protests. The Cold War and very aggressive policy of the Soviet Union gave on chance for significant changes. The importance of political context is clearly visible when looking at the Velvet Revolution.
- December 1989, Romanian Revolution - initial protest was in Timişoara (I could not find the exact size, but several hundreds max, out of 23M => less than 0.05%). It extended to Bucharest where massive protests occurred. Eventually, the regime fell and a (more) democratic regime took its place.
The initial protest size was very small, but the sympathy was very large. The actual change was possible due to very favorable context:
- political context - the Wind of Change was blowing inside the Iron Curtain. See Perestroika and Glasnost.
- economical context - the austerity program to liquidate public debt had made virtually everybody very unhappy.
- social context - people were very unhappy with lack of freedom of speech
So, positive outcome despite initial small protest.
- [21 November 2013, Euromaidan]17 - more than 400,000 protesters at its peak out of 45M population => less than 1%. Public sympathy and support was very large both in Ukraine and outside.
The outcome is very complicated due to the political context (so close to the Russian Federation, Annexation of Crimea etc.)
An important thing to note is that Western countries (through EU and NATO) actually had a meaningful reaction to what happened in Ukraine, by setting up economical and political sanctions.
Conclusion: I would definitely go with the option "There are too many variables to assume a correlation".