Pull out your Tower catalog and look up some models that are the weight of yours and that are a similar type. Look at their suggested engine sizes. Eleven pound models seem to mostly have 1.10-1.40 size 2cycle engines recommended for them or 1.20-1.60 4cycles. So your 1.20 engine sounds about right. As for the Moki....

Weigh it and compare the weight to what is listed for the 1.20-1.80 4cycles that're for sale in catalogs that list weights. Reverse engineering is no real problem. I only looked at one or two models in my Tower catalog so you might check it out a bit more thoroughly.

What is your model? That information alone would get you a lot better answers to your problem.