We utilize individualized, length-sorted (6,5)-chirality enriched single-walled carbon nanotubes (SWNTs) having dimensions of 200 and 800 nm, femtosecond transient absorption spectroscopy, and variable excitation fluences that modulate the exciton density per nanotube unit length, to interrogate nanotube exciton/biexciton dynamics. For pump fluences below 30 µJ/cm2, transient absorption (TA) spectra of (6,5) SWNTs reveal the instantaneous emergence of the exciton to biexciton transition (E11→E11,BX) at 1100 nm; in contrast, under excitation fluences exceeding 100 µJ/cm2, this TA signal manifests a rise time (τrise ~ 250 fs), indicating that E11 state repopulation is required to produce this signal. Femtosecond transient absorption spectroscopic data acquired over the 900 - 1400 nm spectral region of the NIR for (6,5) SWNTs, as a function of nanotube length and exciton density, reveal that over time delays that exceed 200 fs that exciton-exciton interactions do not occur over spatial domains larger than 200 nm. Furthermore, the excitation fluence dependence of the E11→E11,BX transient absorption signal demonstrates that relaxation of the E11 biexciton state (E11,BX) gives rise to a substantial E11 state population, as increasing delay times result in a concomitant increase of E11→E11,BX transition oscillator strength. Numerical simulations based on a three-state model are consistent with a mechanism whereby biexcitons are generated at high excitation fluences via sequential SWNT ground- and E11-state excitation that occurs within the 980 nm excitation pulse duration. These studies that investigate fluence-dependent TA spectral evolution show that SWNT ground→E11 and E11→E11,BX excitations are coresonant, and provide convincing evidence that E11,BX→E11 relaxation constitutes a significant decay channel for the SWNT biexciton state over delay times that exceed 200 fs, a finding that runs counter to assumptions made in previous analyses of SWNT biexciton dynamical data where exciton-exciton annihilation has been assumed to play a dominant role.