I don't think you can get the autorouter to route with a variable trace width. Your best option would be to route the segment from the pad to the wider trace by hand and then run the autorouter. Even so you may have to manually route all the tracks of this type and then tell the autorouter to leave them alone while it does the rest of the routing.

It seems to me @joroenst was asking a similar question about a year ago. It's almost like we need the ability to split a net into 'subnets' that can each have different track widths set-up. Editing the track widths after autoroute is error prone and often doesn't work because substantially different routings are necessary to accommodate the wider tracks. I've found a rather ugly work-around: create a separate circuit for your high-power components and another for your low power stuff. Position components that should be connected (but aren't) close together on the PCB, or position something like a header close to where a connection needs to be made. Set the appropriate track widths in autorouter special nets and let it do it's stuff. It should then be a fairly easy job just to connect the circuits using the PCB track creating tool. You get some quite helpful warning messages along the way, but this seems to work.

@RobertFolkes, Assign the wide track into a dedicated net class then manually route that first. Then tell the autorouter to ignore it so it routes everything else around it. If the wide track needs special treatment then that effectively classifies it as a critical net which should be routed by hand before other tracks anyway.