The more realistic damage scenario for attic storage is not structural failure but, rather, sufficient deflection to pop drywall fasteners. I have not seen it occur but houses are designed to minimize deflection of floors, not to avoid failure. If I can walk on the 2x6s in my attic, and I have, then they can take 200 lbs in about a foot square of space which is more than they will see for storage. I would look at the ceiling joists and make sure they are 2x6s, not 2x4s (I would worry about 2x4s if the span is not real short) and if they are, your concern remains insulation and not structural.
The best way to sister on a 2x6 from an insulation standpoint would be to put it at right angles to the existing 2x6s. There may be a metal connector for this but I did not find any. I put the extra 2x6s directly on top of the existing 2x6s and held in place by constuction adhesive. Small side plates every couple feet of scrap sheet goods, 1/2 to 3/4 thick, and held on with finish nails (until the glue sets and then the glue should hold it). This went pretty fast. You have to avoid putting any real side load on the sistered pieces until the floor goes on because you could break the connection. With the floor in place, it will keep the joists spaced properly and stop them from rolling over. I decided a foot of wood was not terrible insulation.
Jim
The best way to sister on a 2x6 from an insulation standpoint would be to put it at right angles to the existing 2x6s. There may be a metal connector for this but I did not find any. I put the extra 2x6s directly on top of the existing 2x6s and held in place by constuction adhesive. Small side plates every couple feet of scrap sheet goods, 1/2 to 3/4 thick, and held on with finish nails (until the glue sets and then the glue should hold it). This went pretty fast. You have to avoid putting any real side load on the sistered pieces until the floor goes on because you could break the connection. With the floor in place, it will keep the joists spaced properly and stop them from rolling over. I decided a foot of wood was not terrible insulation.
Jim

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