The new Vswethome3d ersion 5.2, February 17, 2016 fixes the problem, But to make it work, I use the added Java Web Start http://sweethome3d.com/SweetHome3D-HiDPIx2.jnlp
This is able to display the user interface of Sweet Home 3D at a twice larger size for users with HiDPI screens under Windows and ...

What finally worked for me was the following:
1) Install Java 21 and Java 64; both if a 64-bit machine).
2) Using Firefox, and get into sweethome
3) use the "ONLINE". This will fire-up JAVA
4) leave Firefox ON, minimize window, and fireup the installed local Sweethome program.
Weird as it sounds ...