It (the 'engrossed copy') was written on parchment rather than paper. Parchment is dried animal skin, and isn't white to begin with although it has darkened somewhat.

The main cause of overall yellowing in paper (not foxing which is a different thing) is due to oxidation of a substance called lignin in the paper which comes from wood. So wood-pulp paper yellows unless the lignin has been removed (as is the case with modern archival paper). But paper wasn't made out of wood until the 19th century; prior to that other sources of fiber were used (cotton, hemp, flax) which don't contain much lignin. So an average paper book page from 1750 would typically be whiter today than one from 1850. If stored well it may not be much darker at all than it was originally. (although paper was never as light then as it is today, where we add white pigments like titanium dioxide)

Here's an example of what 18th century paper can look like, when in good condition.