I wouldn't worry about 'diminishing returns' and would just stick to what code requires, even if your case isn't new construction. You'll be glad you did if it ever comes time to sell. Meeting or exceeding code despite predating those requirements only helps.
So, going from R-27 to R-38 will reduce the heat flux though the roof by about 41% in the most ideal case. That's just for the room, not the walls or the air gaps around the house.
Is it worth it? That depends on the cost. If you're spending $150-180, let's access that and say $165, and say about $65 is what your general per cost (lighting, TV's, washers, dryers, etc, just not coming). Which means about $100 a month is used for AC, give or take. Your roof probably accounts for about half your heating and cooling costs, depending. So you'd probably save about 20% of your energy costs relating to cooling and heating, or around $20 a month, again, rough ball park. That's about $240 a year or $1,200 after 5 years. If it costs 1,200 to install that insulation, that your break even point. If cost double that, like ~$2,400 it would take closer to 10 years. Though, at that point you probably want to start taking inflation into account and do an actual NPV.
Anyway, I would consider if there are other improvements you can do in the mean time that might produce a better value. Both monetarily and in terms of comfort. Not saying there is mind you, just you should consider it.
I wouldn't worry about 'diminishing returns' and would just stick to what code requires, even if your case isn't new construction. You'll be glad you did if it ever comes time to sell. Meeting or exceeding code despite predating those requirements only helps.
So, going from R-27 to R-38 will reduce the heat flux though the roof by about 41% in the most ideal case. That's just for the room, not the walls or the air gaps around the house.
Is it worth it? That depends on the cost. If you're spending $150-180, let's access that and say $165, and say about $65 is what your general per cost (lighting, TV's, washers, dryers, etc, just not coming). Which means about $100 a month is used for AC, give or take. Your roof probably accounts for about half your heating and cooling costs, depending. So you'd probably save about 20% of your energy costs relating to cooling and heating, or around $20 a month, again, rough ball park. That's about $240 a year or $1,200 after 5 years. If it costs 1,200 to install that insulation, that your break even point. If cost double that, like ~$2,400 it would take closer to 10 years. Though, at that point you probably want to start taking inflation into account and do an actual NPV.
Anyway, I would consider if there are other improvements you can do in the mean time that might produce a better value. Both monetarily and in terms of comfort. Not saying there is mind you, just you should consider it.