Does anyone know the cost of a single train ticket from Weeze to Düsseldorf, and is it cheaper/possible to get an open return?
According to the website of the local transport association VRR a single trip costs 16,50€ (just enter the trip into the search mask and click the "E" button to see the price). You can buy the ticket at the station. There is no open return ticket (but if you want to travel on the same day, or more often there are cheaper options, see that website).
If you arrive by plane, please note that Weeze Airport is around 20 minutes by bus from the Weeze train station and at some times it may be better to use the Kevelaer station. Enter Weetze Terminal 1 into the search mask to see those connections. The price is the same.
To answer the second part of the question ("is it cheaper/possible to get an open return?"), the answer is no. In Germany, it is very uncommon that open returns are cheaper. Even buying a non-open return ticket will only lead to lower cost in very few cases.
Note that as neo wrote, you will probably take the bus first, and as the bus and the train are organized in the local transport association VRR, you can buy one ticket for both parts of your journey, which will typically be cheaper.
If you are travelling with 2 people, you should be able to buy a 4-trip ticket that can be used by two people for two trips (as 2x2=4). Please please verify this information with the bus driver, as I cannot find anything about that on the web right now. The cost should currently be 58.60 Euro
There is also the possibility to buy a day-long ticket for all local public transportation in the state NRW for 41 Euro (Schöner Tag Ticket), but the bus driver will probably not sell this. This is good for 5 people, though and includes the bus from Weeze (unless it is operated by a bus company that does not operate within the VRR transport association).
Alternatively, you can buy VRR local transportation association day tickets for 1, 2, 3, 4, or 5 persons at the prices of 26, 30.50, 35, 39.5, or 44 Euros, respectively (again, type "E"). The bus driver should be able to sell these.