The ornamental design for a balloonholderbase, as shown and described.
FIG. 1 is a perspective view of a balloon holder base;
FIG. 2 is a top view of the balloon holder base of FIG. 1; and,
FIG. 3 is a side view of the balloon holder base of FIG. 1.
The broken lines showing of portions of the balloon holder base are included for the purpose of illustrating environmental structure and form no part of the claimed design. All surfaces not shown form no part of the claimed design.