How do tumor cells 'gravitate' towards each other?
It is reported that 99 genes are significantly upregulated in presence of normal gravity, whereas in absence of gravitational force no gene expression is seen in case of T cell activation. Research article attached concluded  that gravity is important for regulating various essential T-cell activation signalling pathways, which play key role in cell proliferation and apoptosis.

Transcription factors like NF-kB, CREB, ELK, AP-1, and STAT are responsible for tumor cell development. And NF-kB and CREB showed gravity-mediated gene expression. As, the PKA
signaling pathway regulates expression of these transcription factor, so it means that gravitational force moderates PKA signalling. And PKA signalling also mediates tumorigenesis. So, by regulating various cell signalling pathways, gravity controls the tumor cells. 

Gravity also modulates the activity of Epidermal growth factor, which are implicated in tumor progression. (Via: https://www.ncbi.nlm.nih.gov/pubmed/7757250)