Errors while performing remote deployment from Eclipse to WebLogic Server

Using local WebLogic server with Eclipse is a piece of cake, especially when using OEPE (the Oracle Eclipse flavor, with all the relevant plugins installed). However, I run into issues while deploying an application to a remote WebLogic server, running on Linux (the machine I used run Windows).
The error was:

weblogic.deploy.api.spi.exceptions.ServerConnectionException: [J2EE Deployment SPI:260041]Unable to upload 'C:workspaceslabWorkspaceNew.metadata.pluginsorg.eclipse.core.resources.projectsHelloWorldbeadepremote_weblogicHelloWorld.war' to 't3://XXX.XXX.XXX.XXX:7041'

java.lang.Exception: Exception received from deployment driver. See Error Log view for more detail.
at org.eclipse.wst.server.core.model.ServerBehaviourDelegate.publish(
at org.eclipse.wst.server.core.internal.Server.publishImpl(
at org.eclipse.wst.server.core.internal.Server$
Caused by: weblogic.deploy.api.internal.utils.DeployerHelperException: The source 'C:DOCUME~1trainLOCALS~1Temp1HelloWorld.war' for the application 'HelloWorld' could not be loaded to the server 'http://XXX.XXX.XXX.XXX:7041/bea_wls_deployment_internal/DeploymentService'.
Server returned HTTP response code: 403 for URL: http://XXX.XXX.XXX.XXX:7041/bea_wls_deployment_internal/DeploymentService
at weblogic.deploy.api.internal.utils.JMXDeployerHelper.uploadSource(
at weblogic.deploy.api.spi.deploy.internal.ServerConnectionImpl.upload(
at weblogic.deploy.api.spi.deploy.internal.BasicOperation.uploadFiles(
at weblogic.deploy.api.spi.deploy.internal.BasicOperation.execute(
at weblogic.deploy.api.spi.deploy.WebLogicDeploymentManagerImpl.deploy(
... 8 more

At first I thought this was caused by the size of the EAR file, but after creating a small HelloWorld.war and getting the same error, I traced it rather quickly.
The problem is network related. First, make sure your browser can connect to the admin console of the remote WebLogic Server (http://XXX.XXX.XXX.XXX:7001/console). If it doesn’t work – configure the proxy, or make the sys-admin open the 7001 port.
If it does work, ensure your eclipse has the proxy configured – using Window/Preferences/General/Network Connections