There's still about a foot of play in the middle.
I put wood glue and finish nails in the loose spindles but very little improvement made. Both newell post are solid.
Wood – How to make a 19′ bannister sturdy
carpentrystairswoodworking
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Heavy duty shelf brackets - supposed support 1000lbs (450kg !)
Wear.
The overlays appear to be solid hardwood. The plywood is a thin veneer over other non hardwood plys. As the steps wear, you run the risk of wearing through the veneer. Even if you don't, if you need to refinish, you again risk sanding through that thin top layer.
In my old house, the bottom stair had a worn dip in the middle (reputedly eroded by my younger son's butt that perched there in his many time-outs). A veneer would have been long gone.
Best Answer
The spindles provide virtually no side-to-side strength; they're all to carry vertical loads. So, improving their attachment won't help at all.
You have two choices:
Install a stronger rail that won't flex as much. This could be a thicker rail, or perhaps an additional strengthening piece added to the bottom.
As @bib suggested, support the rail in the center with a second newel post, well-anchored at the base.
Of course, it's been this way since it was built, and sounds like it's a safety hazard. Talk to the builder?