Lightly weight the tofu, leave it for about 20 minutes to drain.

Literal

Tofu [topic-は] lightly weight [obj-を] do-[and-して], 20 minutes about leave-[and-て] water-drain do.

A recipe instruction. 重し ('weight, something heavy') is the noun form; 重しをする is 'to put a weight on.' ~ほど ('about, approximately') is the standard approximation particle for quantities. 水切り ('draining water') is the standard culinary noun. おく ('to leave, to place') takes に for 'for (a period).' The sentence uses the dictionary-form する at the end, which is typical for recipe instructions — impersonal, imperative-like.