There are many different phenomena in the sentences you list.
Most of them don't really have much to do with prepositions in general, but with specific constructions.
- I let you do it is a complex sentence with an unmarked infinitive complement.
I allow you to do it is a complex sentence with a marked infinitive complement.
X to you a week ago is a simple sentence with a direct object
X and an indirect object you. The verb say does not allow the Dative Alternation.
- I told you
X a week ago is the same structure, with the same objects.
But the verb tell does allow the Dative Alternation, and this is the alternate version.
The unalternated version, I told
X to you a week ago, is also correct.
The "mark" in both cases 1 and 2 is the infinitive complementizer to.
This is not a preposition and does not behave like one.
For one thing, certain verbs (like let) allow one to delete to before infinitive complements,
while most verbs, like allow, require a to to mark infinitives.
In cases 3 and 4, the to is part of a bitransitive (transfer) verb
-- one that has two objects.
The indirect object in such a sentence can usually be marked with to, if it follows the direct object.
However, if it precedes the direct object (the Dative Alternation), then to is not allowed.