There will always be the recommended engine oil that will be specific for the particular engine, even for older ones.
However, there is a certain benefit in using thicker grade oils in older but well-used engines. This is because old engines will most probably have their clearances opened up and larger than when they just came out of the factory.
Also, as engines get old, they will need higher pressure than when they were just new, therefore a thicker grade oil will be helpful in this regard.