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.
I think that the answer to the question is "yes."
I think that the actual use of the veto does signal executive weakness, at least politically. When the president is having to veto bills it probably means his part does not control Congress. It also means that Congress is willing to pass bills that he will veto and that they are trying to make him look bad when he vetoes the bills. That is certainly a weakness -- when you can't control Congress and they are trying to make you look bad.
This will certainly undermine the relationship. Congress puts a lot of work into a bill and then the president vetoes it -- wouldn't you be annoyed? Of course he has the right to do it, but that doesn't mean that it will make Congress happy when he does do it.
I would think that much of this question is contingent on circumstances that exist between the branches. If the relationship between both branches is an overall healthy one, then I think that there would be some understanding that it is not personal or political animosity when the President vetoes a bill, but rather an extension of what he/ she must do. At the same time, I think that it can reflect a great deal of political animosity when a bill passed by both houses of Congress is vetoes by a President. When it is a situation of a "standoff" where the President threatens and then follows through on a veto, it can reflect a fragmented political state.