When you change trace/track width you are only changing a portion of a net to the desired width. Any new traces created on the net will default to the set net width. If you change the net width you are changing all of the existing and future traces on the net to the set net width value.
While routing a trace change the trace width by pressing the w key (keyboard shortcut for segment width) on your keyboard then enter the desired width. This option is also available through the right click context menu.
If changing an already routed a trace mouse over the trace, right-click, and select Segment Width (keyboard shortcut w), Track Width or Net Width from the Context Commands. Selecting Segment Width will change the highlighted segment. The Track Width option will change the entire highlighted track. The Net Width option will change all traces attached to the same net.
Track and net width can also be changed through the properties of a trace. Right click on the trace and selecting Properties. You can change the width on either the Tracks or Nets tab. Changing the Routed Width property on the Tracks tab changes the entire highlighted track. Changing the Width value on the Nets tab will change all traces attached to the same net.
Other fields available for editing on the Nets tab:
Spacing: Controls the amount of space generated around an object connected to the selected net. Use this field to increase the spacing around a track through a filled polygon or to set a specific spacing requirement for the selected net.
Via Size: Controls the default outer diameter for a via created while routing a trace connected to the selected net.
Drill Size: Controls the inner diameter for a via created while routing a trace connected to the selected net.
Net Color: Controls the color of a ratsnest line connected to the selected net.
Assigned to Plane Layers: Internal layers assigned as planes will be listed here. Check the box for the layer to assign the selected net to an internal Plane layer. Internal layers can be assigned as plane layers in the Board Configuration.
Routing Priority: Set the auto-router priority for the selected net.
Do Not Optimize: Check this box to prevent ratsnest lines from jumping to the nearest pin connected to the selected net.
Do Not Autoroute: Check this box to prevent the autorouter from routing the selected net.