NO! I bought a road bike when I weighed slightly more than that and it has been great for me! If you have smooth, well maintained roads to ride on 28 spokes should be fine for a wheel. The 25mm tires will give you a little more comfort because you will be able to run them at a lower pressure. Keep in mind that you can get decent 25mm tires for relatively cheap, so that shouldn't be your deciding factor.

I had never heard of Cube before, but a quick google search showed that the basic peloton model has an 8 speed Claris triple group on it, while the speedster 60 has a 7 speed Tourney double. The 8 speed Claris should be a little better shifting, plus it has better levers, and the triple will provide a lot more gear combinations for climbing up hills and such.

The slightly higher end group set with more gearing options would make me lean towards the Cube.