sistering a 2x6 to current 2x4 rafter
It does not make it as strong as a 2x8, but there's a way you could make it stronger (with some additional materials...)
Beam strength goes directly as width (twice as wide is twice as strong) but as the cube of height (or depth) so twice as deep is 8 times as strong.
Assuming modern planed lumber, 3.5, 5.5 and 7.25 are your actual height for 2x4, 2x6 and 2x8 material, unless they shrunk them again while I wasn't looking.
For a comparison, we'll look at the height cubed, without trying to relate that to anything.
7.25 cubed is about 381
3.5 cubed is about 43 and 5.5 cubed is about 166, for a total when sistered of 209 - quite a bit smaller than 381.
If you put your 2x6 under, rather than beside, your 2x4s, and then plate them together with some OSB or plywood, you get roughly in the ball park of 729 for the depth cubed.
Indeed, you could come quite close to a 2x8 just by putting 2x4s under the 2x4s, if they are well-bonded with plates, and if the plates are large enough they also add to the stiffness. You can also follow that path to building a small truss in place, which I'd not advise for a house, but it's quite feasible for a carport unless you are in the sort of jurisdiction that will require permits and engineering drawings for reinforcing your carport roof, (that seems unlikely, since it was underbuilt to begin with.)