The plans, which the government says are needed to curb overreach by judges, have drawn fierce opposition from groups including lawyers, and raised concerns among business leaders, widening already deep political divisions in Israeli society.
"I'm here tonight protesting against the transition of Israel from a democracy to an autocracy," Dov Levenglick, 48, a software engineer told Reuters in Tel Aviv.
"It's a disgrace, it shall not stand."
Netanyahu has dismissed the protests as a refusal by leftist opponents to accept the results of last November's election, which produced one of the most right-wing governments in Israel's history.
The protesters say Israeli democracy would be undermined if the government succeeds in pushing through the plans, which would tighten political control over judicial appointments and limit the Supreme Court's powers to overturn government decisions or Knesset laws.
"They want to tear up the judiciary system of Israel, they want to tear up Israeli democracy, and we are here every week in every weather ... to fight against it and to fight for Israeli democracy," Hadar Segal, 35, told Reuters in Tel Aviv.
Opposition leader Yair Lapid joined demonstrations in the coastal city of Haifa, where he said protesters "came to save their country, and we came to protest with them."