How much weight exactly are you wanting to add?
I have a Kenwood KP-9010 and Kenwood sold quite a few accessories one could purchase to enhance the performance of these DD tables.
All the accessories that were sold for the L07 Kenwood's would work on the KP-9010, KP-1100 and maybe others.
Pretty sure the DD motor on your 59L is a high torque model. I'm not gonna say "no problems" as I have no idea how much weight you're talking about....
Has your table been restored? Caps, resistors, brought back to spec?
If not, and you're running all original electronic parts inside the TT I'd probably not try at all. If you're thinking of adding weight I'd have the TT internals restored/upgraded first.
Aldo