Thanks for the save file with your report!
I was able to reproduce the issue on your save with your mod set, on 2.0.77. It should be fixed in the next release of Better Belt Balancer.
The tl;dr is that it's a compatibility issue with HandyHands. Details follow.
BBB creates a two-way link between two prototypes. To adopt Belt Balancer 2/3 saves and blueprints BBB keeps a hidden compatibility item and entity, both named balancer-part. The item placed BBB's part entity, and the entity was placeable by BBB's part item, so the engine listed each of the two entities as placeable by the other's item.
HandyHandsRefactored has a pass that runs every 60 ticks while the personal roboport is enabled, for a character controller only, and that pass walks each quickbar item to its entity and on to the items that place it, inserting and deleting entries of the table it is iterating. On that two-element cycle the walk never finishes. That is why the roboport toggle, the part in the quickbar (a filter slot is enough, no item needed) and the editor all mattered, and why the log stays empty: nothing errors, one Lua loop simply never returns. Removing the balancers cannot help, since the loop is over prototypes rather than entities.
The fix points the compatibility item at the compatibility entity instead, which the mod already converts to a real part on the next tick, so nothing changes in play. As a a short-term workaround, you can take the balancer part out of the quickbar while the roboport is on or turn off HandyHands.
The loop on HandyHands' side is unsafe for any pair of prototypes shaped like this, so I opened a PR to fix the issue there to improve HandyHands compatibility with other mods going forward.
