whether to

  1. I do not know whether to weep or to laugh.
  2. I do not know whether to weep or laugh.
    Which one is correct sentence? OR are both correct?
    Thanks.

Both possible, 2 is usual, you don’t need to repeat ‘to’.
As this is conversational in nature, usually the main verb would be contracted:
I don’t know whether to weep or laugh.

(a) you don't have to repeat 'to'.
(b) you needn't repeat 'to'
(c) you haven't got to repeat to'

Beeesneees, I have two questions:

1) can I use one the three options above in place of the original sentence? Are they equally interchangeable?  Through various grammar books I have learnt that they are synonymous structures, however, I would like to know whether they are interchangeable in practice. 

 2)
 Also, can I change 'as' to the following?

(a) Since; (b) Because;  (c) Inasmuch as        

                        Thanks.
  1. Yes, you can use any of them.
  2. Yes to (a) and (b) though © does not have quite the same meaning. ‘Inasmuch as’ wouldn’t be used here, because there is no directly preceding comment. (It’s used to say why the preceding comment is true, so the sentence would have to be reversed:
    It’s perfectly reasonable to use a contraction here inasmuch as the sentence is conversational.

I wouldn’t describe the above as ‘contracted’. The second ‘to’ is redundant because both infinitives are dependent on the same verb.

Gussie

It is this that is the contraction, Gussie:
I don’t know…