Which DNA sequence will have higher melting temperature: CCCCCC... or GCGCGC...?
The dependence of melting temperature on different dinucleotide pairs was experimentally measured; the meting temperature calculator is based on those results. Based on these results, you would see that a GC dinucleotide pair would differ from GG and CC pairs. Possibly, this is because of steric effects and stacking conformations.

SantaLucia (1998; author of the nearest neighbour model) has referred to different experimental studies from which the values were obtained, in the Table-1 of the paper.