Question arise:
What is SAP NetWeaver?
SAP NetWeaver is an integrated technology platform which provides development environment for integrating business processes and databases from no of environments like
Microsoft’s .NET, IBM’s WebSphere,  Sun’s Java technologies and of course SAP.
More Details
Now back to our post’s title
Does QTP support NetWeaver? Yes.
Do we have any add-in for NetWeaver from HP? No
How would NetWeaver work with QTP? Simply find out the technology NetWeaver integrates with. If suppose it is SAP use SAP add-in, for .NET use .Net add-in and similarly for Java use Java add-in.

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Check the up-to-date matrix for the currently supported versions of SAP by QTP (UFT)