We investigate two-photon absorption (2PA) in a series of fluorenyl-based 9,9-diethyl-2-ethynyl-7-((4-R-phenyl)ethynyl)-9,9a-dihydro-4aH-fluorene chromophores with R being various electron donating (ED) and electron withdrawing (EW) groups. We use wavelength-tunable femtosecond laser pulses to measure the 2PA cross sections in the lowest dipole-allowed transition and show that the substituents with stronger ED or EW character enhance the peak 2PA cross section (up to sigma(2) similar to 60-80 GM) while the neutral substituents lead to smaller cross sections, sigma(2) < 10 GM. We apply two-level approximation to establish a quantitative relation between the 2PA in the pure electronic transition (0-0) and the corresponding change of the permanent electric dipole moment upon the excitation (Delta mu). This relation is elucidated by comparing Delta mu values obtained from the 2PA measurements with quantum-chemical calculations and with measurements of solvatochromic shifts in a series of solvents. We show that the calculated Delta mu correlate well with the values obtained from the 2PA spectroscopy. The Delta mu values obtained from the solvatochromic shifts agree well with the above two methods for the chromophores with neutral or weak EW or ED substituents. On the other hand, stronger EW or ED end groups give much larger Stokes shifts, which lead to an overestimation of the Delta mu values. We tentatively attribute this effect to the excitation-induced electronic density change occurring predominantly at the substituent side of the molecule, which causes the effective point dipole associated with the Delta mu to interact more strongly with the surrounding solvent.