Ask Mr. Smarty Plants

Solanum elaeagnifolium (Silverleaf nightshade), is called in our Native Plant Database "an aggressive, poisonous weed...".  It isn't listed in Poisonous Plants of North Carolina (probably because silver nightshade isn't prevalent in the Eastern US), but the closely related Solanum carolinense (Carolina horse-nettle) is listed as Toxic Only If Large Quantities Eaten.  Silver nightshade is listed in the Plants of Texas Rangelands as a toxic agent that:

"...has reportedly poisoned horses, sheep, goats, cattle and humans. However, sheep and goats are more resistant than cattle, and in controlled experiments, goats were not poisoned at all. Its toxic agent is solanine. The leaves and fruit are toxic at all stages of maturity; the highest concentration is in ripe fruits. In some instances, an animal can be poisoned by eating 0.1 to 0.3 percent of its weight in silverleaf nightshade."

The California Poison Control System gives all the Solanum species a Toxicity Rating of 1, meaning that the plants in the Genus Solanum "may cause serious illness or death".

The Veterinary Medicine Library of the University of Illinois lists all Solanum species and says that risk of poisoning depends on the species, the maturity of the plants and other conditions. They also say that for S. eleagnifolium it is the ripe berries that are more poisonous than the green unripe berries—this is in contrast to most other species of nightshade (and in contradiction of Plants of Texas Rangelands information).  They also mention that silver nightshade can be poisonous at only 0.1% of the body weight.

Pennsylvania Poisonous Plants Database doesn't list S. eleagnifolium, but does list S. carolinense, S. nigurm [synonym=Solanum americanum (American black nightshade) and S. dulcamara (Bittersweet nightshade). S. tuberosum (potato) is also included for the potential of poisoning from potatoes with skins that have turned green due to sun exposure from growing too near the surface.

You can see my answer to a recent question about S. americanum (American black nightshade) and my advice about eating just one berry.  I don't know what part of the silver nightshade you are thinking of using in making your cheese, but my advice to you is to read the information about the toxicity of all the Solanum species and use extreme caution before trying even a small amount of the plant.   In fact, if I were you, I would avoid consuming even a small amount of it.