The ice is so thin it probably can't support your weight.

Literal

Ice [topic-は] very thin [because-ので] your weight [object-を] support-unable [probably-だろう].

薄いので gives the reason. 支えきれないだろう uses きれない ('unable to completely do') + だろう (conjecture). 君の体重 uses the casual second-person 君.