Weight multiplicities in the A2 tensor square of highest weight (2,0)

The tensor square has fifteen distinct weights: three outer corners of multiplicity one, six near-corner edge weights of multiplicity two, three edge midpoints of multiplicity three, and three interior weights of multiplicity four. In the irreducible components only $R(2,1)$ is weight-degenerate: $(1,0),(-1,1),(0,-1)$ each have multiplicity two. All weights of $R(4,0)$ and $R(0,2)$ have multiplicity one.