How to understand this grammatical explanation about infinitve and participial

Question

[52] i a. I like to stay home at weekends. b. I like staying home at weekends.
      ii a. I’d like to be a politician. b. I’d like being a politician.

With [i] there are many contexts where [a] and [b] would be equally appropriate, but there are also some favouring one or the other. Suppose you ask me to go bushwalking next week-end but I wish to decline: [a] would here be more appropriate than [b]. Conversely if I am currently enjoying a week-end at home [b] is more appropriate than [a].
    The infinitival is more associated with change, the gerund-participial with actuality. Thus someone who has recently turned forty or got married might say I like being forty or I like being married. An infinitival would be strange here, suggesting repeated changes from not being forty or married to being forty or married. In this case the meaning is close to that of enjoy, which only allows gerund-participials. Would like, by contrast, projects into the future and resembles a verb of wanting, with a strong preference for the infinitival, as in [iia]; [iib] is possible, but the interpretation is roughly “I’d like/enjoy the life of a politician”. If we change the examples to I’d like to start the meeting a little earlier this week the gerund-participial becomes quite implausible: I’d like starting the meeting a little earlier suggests that the starting is itself something to be enjoyed, which is an odd idea.

  Hate with a to-infinitival has an idiomatic use seen in

[53] I hate to tell you this, but your battery is flat.

This can be thought of as involving projection into the immediate future: “I’m going to tell you, though I hate having to do so”. What is special about this use (virtually confined to the 1st person) is the combination of simple present tense in the matrix and single dynamic event in the complement - constrast [52ia], where we have repetition of staying home; other verb of liking and not liking do not allow this pattern, though it is found with adjectives: I am happy / ✲like to tell you that you’ve passed your test (cf. also regret in [56] below).
(The Cambridge Grammar of the English Language)

Question 1) “suggesting repeated changes from not being forty or married to being forty or married” -> what does this mean?
Question 2) “In this case the meaning is close to that of enjoy” -> What ‘case’ does this sentence indicate? Is it an infinitival (I like to be forty, I like to be married) and the infinitival means ‘enjoy’?

Answer 1

"An infinitival would be strange here, suggesting repeated changes from not being forty or married to being forty or married."

This means that the infinitival implies that you commonly switch between being/doing [x] and not being/doing [x], which doesn't make sense for age or marital status; you don't become 40 for a while and then stop being 40 for a while, and at least in most cases a person isn't married and then not married multiple times in a short period. Here are some examples that do change:

I like to eat sandwiches.

I like to sleep in on Saturdays.

I like to write poetry.

It is likely that you do not spend all your time eating sandwiches or writing poetry, and since it isn't always Saturday you can't always be sleeping in, either. These are examples of states that change. You could also use the -ing form in all of these cases (I like eating sandwiches), but the point the article is making is that while either form is appropriate for things that change, the infinitival form is not appropriate for things that do not often change (being married or being a certain age).

"In this case the meaning is close to that of enjoy"

This means that when you say I like being 40 you mean I enjoy being 40, and when you say I like being married you mean I enjoy being married.