Jefferson never trusted Burr.
He was effectively shut out of party matters.
As vice president, Burr earned praise from some enemies for his even-handed fairness and his judicial manner as President of the Senate; he fostered some practices for that office that have become time-honored traditions.
Burr's judicial manner in presiding over the impeachment trial of Justice Samuel Chase has been credited as helping to preserve the principle of judicial independence that was established by Marbury v. Madison in 1803.
One newspaper wrote that Burr had conducted the proceedings with the "impartiality of an angel, but with the rigor of a devil".

Burr's farewell speech in March 1805 moved some of his harshest critics in the Senate to tears.
But it was never recorded in full, and has been preserved only in short quotes and descriptions of the address, which defended the United States of America's system of government.
Jefferson never trusted Burr. He was effectively shut out of party matters. As vice president, Burr earned praise from some enemies for his even-handed fairness and his judicial manner as President of the Senate; he fostered some practices for that office that have become time-honored traditions. Burr's judicial manner in presiding over the impeachment trial of Justice Samuel Chase has been credited as helping to preserve the principle of judicial independence that was established by Marbury v. Madison in 1803. One newspaper wrote that Burr had conducted the proceedings with the "impartiality of an angel, but with the rigor of a devil".
Burr's farewell speech in March 1805 moved some of his harshest critics in the Senate to tears. But it was never recorded in full, and has been preserved only in short quotes and descriptions of the address, which defended the United States of America's system of government.
Aaron Burr