She [topic-は] eyes [at-に] tears [object-を] floating TV [object-を] was-watching.
目に涙をうかべてテレビを見ていた — 浮かべて ('with tears welling up') in te-form sets the emotional state for watching TV. うかべて is written in hiragana rather than the kanji 浮かべて, a common stylistic choice in casual writing.