In "Romeo and Juliet", why does Capulet suddenly decide to accept Paris's offer?In Act 1, Capulet was not eager to see Juliet married.

No, you're absolutely right: in Act 1, he gives Paris the clear information that Juliet isn't ready for marriage:

My child is yet a stranger in the world,
She hath not seen the change of fourteen years;
Let two more summers wither in their pride
Ere we may think her ripe to be a bride.

And then, a little later, Capulet tells him about the party and makes two further arguments:

But woo her, gentle Paris, get her heart;
My will to her consent is but a part.
An she agree, within her scope of choice
Lies my consent and fair according voice.
This night I hold an old accustom'd feast,
Whereto I have invited many a guest,
Such as I love; and you among the store,
One more, most welcome, makes my number more.
At my poor house look to behold this night
Earth-treading stars that make dark heaven light.
                                         ...Hear all, all see,
And like her most whose merit most shall be;
Which, amongst view of many, mine, being one,
May stand in number, though in reck'ning none.

Paris should woo Juliet himself, Capulet argues - but also, he should set her in the context of other women at the party, and see who he likes best. Juliet might be counted as "none" when put in the context of "many".

Then, later in the play, with Tybalt dead, Capulet entirely changes his tune. The text doesn't give a clear motive for this: it may be simply that he wants to strengthen his house after the death of Tybalt, his kinsman. But I think there's a better explanation, with a little close reading, to be found. Remember that Paris is the Prince's kinsman, and a lot richer than the Capulets. He's a good marriage prospect, even if Capulet isn't too keen to let his daughter go.

And, on the night of Tybalt's murder, Capulet is making excuses - and yet, more weirdly, Paris is there, at the house, even though Tybalt only died that day. Is he losing patience?

CAPULET
Things have fall'n out, sir, so unluckily
That we have had no time to move our daughter.
Look you, she lov'd her kinsman Tybalt dearly,
And so did I.

PARIS
These times of woe afford no time to woo.
Madam, good night. Commend me to your daughter.

How does Paris speak that line? "These times of woe afford no time to woo". It could be gentle and conciliatory, but it could also be hostile. Note he doesn't say good night to CAPULET, but only to Lady C. Is he about to leave, never to return?

LADY CAPULET
I will, and know her mind early to-morrow;
To-night she's mew'd up to her heaviness.

Lady C promises to have the key info first thing in the morning. Is she trying to keep Paris on board? Is he perhaps already getting his coat? Well, something certainly prompts the next line of Capulet's:

Sir Paris, I will make a desperate tender
Of my child's love.

And you know what comes next. So that would be my interpretation: in a play full of hasty young people, Paris is about to lose his patience and go off and find someone else to marry. And Capulet just won't have that happen.