My target is to be able to connect the usb on a Oregon Scientific weather station WMR (88 or similar) in order to extract the weather informations available
A link to the device in question would be useful. But, in general devices like this are USB slaves. The intent is to have some USB Master (like a PC) control the device, making it do something or say something.
The Arduino has a place to connect a cable that has a USB connector on one end, but, it, too, is a USB Slave.
One USB slave can not make another USB slave do anything. Only a USB Master (Host) can control a USB slave.
Fortunately, sparkfun has a USB Host shield for the Arduino. Unfortunately, writing device drivers is not trivial. So, getting data from the weather station is going to be a challenge. If there is information available on how the weather station gives up data on the USB port, life will be much easier. If not, you've got a big task ahead.