�at� is usually associated with British English, �on� is usually associated with American English (at least according to Michael Swann - p.296 of Practical English Usage, 3rd ed.)
1) She is working during the weekends -
a) while �weekends � sounds a little odd, it would indicate that she works every weekend, so her schedule will not allow for other activities across ongoing weekends.
b) If it were �during the weekend � indicates she is scheduled or expected to work on the specific weekend under discussion (prescriptive grammar - singular weekend) OR that it is an ongoing situation (according to descriptive grammars - i.e. how native speakers use the language)..
c) �She works during the weekend� indicates she is scheduled or expected to work on the specific weekend under discussion (prescriptive grammar - singular weekend) OR also that it is an ongoing situation (according to descriptive grammars - i.e. how native speakers use the language).
2) She works IN the weekends - definitely should be ON -
a) means that it is an ongoing circumstance that she works every weekend. �She works on the weekend � indicates she is scheduled or expected to work on the specific weekend under discussion (prescriptive grammar - singular weekend) OR also that it is an ongoing situation (according to descriptive grammars - i.e. how native speakers use the language).
b) �She is working ON the weekends � indicates an ongoing circumstance or expectation that she works on every weekend.
3) She is working AT the weekends -
a) means that it is an ongoing circumstance that she works every weekend - plural weekends. �She works AT the weekends also means this!
b) �She is working AT the weekend � indicates she is scheduled or expected to work on/over/during/at the specific weekend under discussion (prescriptive grammar - singular weekend) OR also that it is an ongoing situation (according to descriptive grammars - i.e. how native speakers use the language).
Without providing context it is not actually possible to determine the 100% correct interpretation in terms of native English communication.
In terms of prescriprive grammar (or the strict grammarians �rules of grammar � - which is not actually how native speakers actually consistently speak & is commonly called �descriptive grammar � by many linguists) then the meanings could be derived as per the a) responses above. This does not mean those responses are actually how the language is used by native speakers!!!
Regards,
AB
That was great! 
