Cleft sentences (main and subordinate clauses analysis)

A few general remarks about it-clefts

According to CGEL (p. 1414),

'Cleft' is a process term: the idea behind it is that a cleft clause is formed by dividing a more elementary clause into two parts.

Take the example of the non-cleft sentence

[A] I bought a red wool sweater.

and its it-cleft version,

[B] It was a red wool sweater that I bought.

Here [B] can be thought of as as being formed from [A]

by dividing it into the two parts a red wool sweater and I bought. One of the two parts, here a red wool sweater, is foregrounded, and the other, I bought, backgrounded. Syntactically, the foregrounded element is made a complementof the verb be in its specifying sense - an internal complement in the it-cleft. … The backgrounded component, by contrast, is subordinated by being placed in a relative construction.

CGEL then continues (pp. 1417-1418):

It-cleft clauses have it as the subject of the matrix be clause, with the relative clause appearing in extranuclear position at the end. The it in subject function can be thought of as a place-holder for the variable, which is defined in a relative clause that is not syntactically part of the subject.
…
The foregrounded element in an it-cleft serves as the antecedent for a gap or pro-form in the relative clause, but this relative clause represents a distinct type, differing in certain respects from ordinary relative clauses, whether integrated or supplementary. Most importantly, it allows a somewhat broader range of elements to be relativised.

Your first sentence: a foregrounded PP

A little later on, CGEL says that preposition phrases (PPs) are the second most common type of element forefrounded by an it-cleft. (Note that CGEL analyzes because as a preposition, in contrast to traditional grammar.) One of the examples provided is

It's because you stood up for yourself that you were sacked.

about which CGEL says that it is of the form 'because + clause complement'. This is just like your first sentence,

It was because you are clever that I married you.

Your second sentence: a foregrounded gerund-participal clause

In your second example, it is a non-finite clause that is foregrounded. It corresponds to the following example in CGEL (p. 1418):

It was listening to Sue's story that made me realise how lucky we have been.

This is a gerund-participal clause, about which CGEL says,

Gerund-participials [like in the sentence above] are permitted, albeit uncommon. Compare, for example, the non-cleft They began playing golf with the it-cleft *It was playing golf that they began. The inadmissibility of the latter correlates with the fact that the complement of catenative begin cannot be questioned with what (They began playing golf cannot be used to answer the question What did they begin?), and insuch cases there is no pseudo-cleft either (*What they began was playing golf).

(1) [[It was because [you are clever]] [that I married you]].

(2) [[It was [learning French]] [that I found tiring].

Brackets surround the various clauses.

In both examples, the main (matrix) clause is the sentence as a whole.

Within the main clause, there is a head clause and a dependent relative clause, the former containing an embedded clause. Both head and dependent clauses are subordinate to the main clause.

In (1) the head clause is "It was because you are clever", within which is the embedded subordinate content clause "you are clever" functioning as complement of "because". The dependent relative clause is "that I married you".

In (2) the head clause is "it was learning French", within which is the embedded subordinate non-finite clause "learning French" functioning as predicative complement of "was". The dependent relative clause is "that I found tiring".

Note that in an it-cleft construction the relative clause does not form a constituent with its antecedent, i.e. it does not modify it.