I believe driveline backlash like this is a combination of wear at several locations. I have the same problem with my 190E-2.3 Sportline 5-speed now showing almost 230,000km. I noticed service documents from the previous owner mentioning the problem. In response, the previous owner had the flex couplings replaced, engine mounts replaced and differential overhauled. Despite all this there is still backlash which I have simply learned to live with. Unless you are rough with it (or have clutch shudder as mine does cold after sitting for several days) there is no obvious problem. Checking components underneath does not reveal any one problem area. Instead, a combination of wear at various points appears to add up to cause the problem. I believe much of it may well be in the various splines, particularly on the rear axles. Remember also that backlash before the differential needs to be around 3 times more than backlash after the diff to have the same effect due to the gear ratio of the diff. My high kilometre 350SLC has noticeable wear in the rear axle splines which gives consderable backlash, masked only by the fact it has auto rather than manual transmission. As for the balance weight at the front flex coupling, I believe this was unique to the manual versions. My manual '90 190E has it whereas my auto '90 300TE (and '73 350SLC) do not.

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107.023: 350SLC, 3-speed auto, icon gold, parchment MBtex (sold 2012 after 29 years ownership).
107.026: 500SLC, 4-speed auto, thistle green, green velour.
124.090: 300TE, 4-speed auto, arctic white, cream-beige MBtex.
201.028: 190E 2.3 Sportline, 5-speed manual, arctic white, blue leather.
201.028: 190E 2.3, 4-speed auto, blue-black, grey MBtex.
201.034: 190E 2.3-16, 5-speed manual, blue-black, black leather.