Learn Polish: Weź to lekarstwo, bo jesteś chory. - Take this medicine, because you are sick.

Weź is the imperative (command) form of the verb wziąć (to take), used when speaking informally to one person. Command forms can be quite irregular in Polish, so this is a great one to memorize! If you were telling a group of people to take their medicine, you would add -cie to make it weźcie.

Why do we use to before lekarstwo instead of ten or ta?

The word lekarstwo (medicine) ends in -o, which makes it a neuter noun. The word for "this" has to match the gender of the noun, so we use the neuter form to instead of the masculine ten or feminine ta.

Is the word chory used for anyone who is sick?

No, chory is the masculine form of the adjective, so this sentence is being spoken to a male. If you were telling a female to take her medicine, you would use the feminine form chora and say: Weź to lekarstwo, bo jesteś chora. The command word weź does not change based on gender.

What case is to lekarstwo in here?

It is in the Accusative case, because it is the direct object of the verb (it is the thing being taken). It might look like nothing changed, but that is simply because neuter nouns, and the word to, look exactly the same in the Accusative case as they do in the basic Nominative dictionary form.