It's important to understand the difference between a Relate and a Join, and I'm somewhat unclear on the current setup of your data ("organized by month" how - as rows or columns?).
If your weather data is in separate tables for each month or all months are in the same table with a row for each month, with fields called speed, temp, etc. then you would need to use a Relate. This is because for every one station in your points there are many values (records) for the same point ID in the other table.
This is a one-to-many relationship, which ArcGIS doesn't handle well in a Join - it returns the first matching record found and ignores the rest. For this reason a Relate cannot be 'made permanent' via a Join, and why they are two separate tools/processes. A one-to-many is usually addressed with a Query Table, which basically creates a new table with a record for each possible combination from the two sources. For example if you have one station point and that point has six records in the other table, your new table will end up with six different points in the same place (depending on tool options).
If your weather data is in a single table and your fields are more like Jun12_temp, Jun12_speed, etc., then a Join would work because your table would have one record for each station to match each station point, a one-to-one relationship. All the different readings at all the different times would be attributes of a single point, so just Joining that table to the points via Station ID would get you a useable dataset for interpolation - you'd simply point at the desired field for your Z values.
As far as I know, geoprocessing tools cannot access data through a Relate - it's more of a lookup/access/select kind of function than a use/analyze. In order to run an interpolation on specific values, you'll have to do some pre-processing of your data either to create several separate point feature classes or combine all the reading data into a single table with unique field names.