What does aguantarme mean?
It was used in the following context: te amo mi amor gracias para aguantarme y por ser lindo cuando estoy pesada un besito grande
In that context it means "put up with me".
I love you, dear. Thank you for putting up with me. And for being sweet when I am down. A big kiss.
Aguantar means "to bear with" and aguantarse means "to hold back" although I have rarely heard aguantarse. Having said that what does "Tuve que aguantarme todas las lágrimas" mean....I had to hold back my tears, or I had to bear with my tears?
It means to "hold back" but you can translate the rest yourself here. Also you can simply doublclick on the words to get their meanings.