While presidents can exercise the veto to influence Congress, does the use of veto power signal executive weakness or undermine relations w/congress

I don't think it signals weakness, because the veto is so
often effective.  It is very difficult and often impossible for both houses of Congress
to amass the 2/3 vote needed to override a Presidential veto.  So in this way, a veto
signals strength.  We also must remember that Congress is often controlled by a party
other than the one that controls the White House.

A veto is
stronger if used more rarely, because the threat of a veto is often
more effective at moving votes in Congress the way a President wants them to move, or
will  allow him to get changes into the legislation before the vote.  Once the veto is
used, Congress has no more incentive to negotiate with the President about the bill.  In
this way, it can undermine relations with Congress.