Removing a wall
You need to determine the load requirement for an attic in your jurisdiction. Either review the code, or talk to the building inspector. I assume you need a permit, so you are going to need to file plans with the building inspector anyway, so best to discuss the loading requirement sooner rather than later. The load requirement will depend on what code is being followed, current IRC imposes a higher load for attic space than older code, so the required header size is larger.
You need to determine the tributary area to the header. Assuming you have floor joists above, the tributary area is likely to be half the width of the attic above, but this needs to be verified. Once you know the tributary area, and the load, you can compute the required header size. Since you don't want to hire an engineer, either you are going to have to perform the computations, or you can go to a lumber yard and ask them to perform the computations, based on the assumption that they will supply the required lumber. In my town, you need to show the inspector the calculations before you can get a permit, but it may be different where you live.