1. A system comprising: a computer-readable memory storing executable instructions; and one or more processors in communication with the computer-readable memory, the one or more processors programmed by the executable instructions to at least: execute a server-side browser application; obtain, by the server-side browser application, a request for a network resource from a client-side browser application executing on a client computing device, wherein the network resource can be processed with a plurality of processing actions, wherein the server-side browser application is configured to perform each of the plurality of processing actions, wherein the client-side browser application is also configured to perform each of the plurality of processing actions, and wherein the plurality of processing actions comprises at least one of: parsing a markup document, generating a document object model, generating a structural representation of a display style; executing embedded script code, or generating a display layout; and responsive to the request for the network resource: determine a context of the request for the network resource, wherein the context comprises at least one of: an account level, a processing capability of the client computing device, an availability of a network connection, pricing plan information, an available bandwidth, or prioritization information; determine a browse session configuration based at least partly on the context of the request for the network resource, wherein the browse session configuration specifies a first subset of the plurality of processing actions to be performed the server-side browser application and a second subset of the plurality of processing actions to be performed by the client-side browser application; process, using the server-side browser application and the browse session configuration, the network resource by performing the first subset of the plurality of processing actions to generate an offline content representation; transmit the offline content representation to an offline browse storage component, associated with the client computing device, to be accessed when a network connection to the server-side browser application is unavailable; process, using the server-side browser application and the browse session configuration, the network resource by performing the first subset of the plurality of processing actions to generate a processing result; and transmit the processing result to the client-side browser application, wherein the client-side browser application performs a remaining portion of the plurality of processing actions to display a representation of the network resource at the client computing device.