Sarah

업다 means carrying on one's back in Korean. I think it can also mean sharing the weight of another's life, as a metaphor for unconditional love. Rather than using fancy strollers that most moms want, Mijeong is saying she wants to carry her child's weight by herself with her whole body. She doesn't care about what others think, she just wants to love her child. Wanting to carry Gu at one year old may mean that she wants to share and heal the burden that Gu had to face as a child. Judging by his past as a gangster, Gu obviously had a terrible childhood and has no experience of being loved unconditionally. This is why Gu feels scared when he's happy with Mijeong, which she can see through. Therefore, Mijeong is reassuring Gu that she loves him no matter what.