stardew-valley – Max Friendship Levels For Bachelors And Bachelorettes In Stardew Valley

I believe you can only reach (and subsequently see) the 10-heart cut-scenes if you give each marriage candidate a bouquet. Here's a quote from the developer on a thread from Reddit:

wait, you can get to 10 hearts without giving a bouquet? That was the whole reason for the bouquet mechanic... to prevent players from seeing the 10-heart event unless they show their romantic interest in someone. whoops

From his comment at the end, it sounds like it might be possible (via a bug) to see those cut-scenes without the bouquet, but that will likely be fixed in a future update if history serves.

Update: Here's another comment from the developer on this (again, from Reddit):

I think the ability to non-romantically befriend the marriage candidates to 10 is a great idea, the only thing stopping me from doing it is the large amount of work involved. It might happen some day though. Now if only I could get my hands on Maru's cloning device...

Update 2: I spotted this in the change log for the upcoming 1.07 patch (available April 4, 2016):

The last two hearts are now greyed-out for marriage candidates until you give them the bouquet.

That confirms to me that hearts 9 & 10 are indeed unreachable without a bouquet.

This is in fact intended.

As DanmakuGrazer said, by increasing your relationship with your spouse, it will eventually reach 13 hearts. When this happens, the relationship becomes "capped" like every other relationship: it won't naturally decay. (It can still decrease due to actions such as the character witnessing you digging through trash, or if you give gifts to bachelor/ettes while married.)

Getting your spouse's relationship to 13 is a requirement for

getting a stardrop. More accurately, once your spouse is at 13.5/12 hearts, you'll receive the stardrop. (H/T @Pathoschild.)

In fact, in the past, instead of being represented as 13/12, this would be shown

as a stardrop icon.