Increasing the bypass actually decreases the thrust. A good example is the CFM56-5B variant (sortable table on Wikipedia). The reason is easy to grasp, the more air bypasses the core, the lower the core's power.
The next question would be how did the TF39 achieve higher bpr and thrust? Through an extra half-fan and extra turbine stage. It will make sense by viewing the cross section drawing and front view below:
(flightglobal.com) CF6 top half, TF39 bottom half.
(wikimedia.org) TF39 front view.
This covers the thrust/bpr and the how, on to the why. The DC-10 (the launch CF6 customer) cruised at a higher Mach number (M0.82-0.88) compared to the Galaxy's M0.77. At high Mach numbers, a lower bpr is more efficient (think turboprop with a 40:1 bpr and a jet) -- speed is the key here.
Other reasons include the airlines' desire to have one fan with easy access, and fewer parts to deal with. Flight summarized it in 1969 as follows:
General Electric CF6 in -6 form at 40,000 lb thrust for take-oft was the engine specified by American Airlines and United Air Lines in their launching orders for the DC-10-10. Whereas the TF39 has a large two-stage front fan assembly the CF6-6 has an entirely new single-stage fan with a small single-stage booster fan. The change brings down the by-pass ratio from 8.0 to 6.2 and permits the deletion of a stage from the compressor; take-off thrust is reduced from 41,000 lb (TF39) to 39,400 lb (CF6-6) but the cruise thrust/s.f.c. characteristics are improved at higher Mach. Other changes include fan blade containment built-in to the casing; substitution of a gearbox to suit airline requirements; control system adapted to airline practice (idle and reverse added); increased accessibility of fan and gearbox; external piping; and a review of all materials for increased life.
The beefier CF6 you mention -- the CF6-50 -- again increased the airflow reaching the core (which reduces the bypass air) by adding booster stages behind the fan. This is how to get higher thrust with minimal changes.