Half-filled Landau levels admit the theoretically powerful fermion-vortex duality but longstanding puzzles remain in their experimental realization as $ u_T=1$ quantum Hall bilayers, further complicated by Zheng et als recent numerical discovery of a
n unknown phase at intermediate layer spacing. Here we propose that half-filled quantum Hall bilayers ($ u_T=1$) at intermediate values of the interlayer distance $d/ell_B$ enter a phase with textit{paired exciton condensation}. This phase shows signatures analogous to the condensate of interlayer excitons (electrons bound to opposite-layer holes) well-known for small $d$ but importantly condenses only exciton pairs. To study it theoretically we derive an effective Hamiltonian for bosonic excitons $b_k$ and show that the single-boson condensate suddenly vanishes for $d$ above a critical $d_{c1} approx 0.95 l_B$. The nonzero condensation fraction $n_0=langle b(0) rangle ^2$ at $d_{c1}$ suggests that the phase stiffness remains nonzero for a range of $d>d_{c1}$ via an intermediate phase of paired-exciton condensation, exhibiting $langle bb rangle eq 0$ while $langle b rangle =0$. Motivated by these results we derive a $K$-matrix description of the paired exciton condensates topological properties from composite boson theory. The elementary charged excitation is a half meron with $frac{1}{4}$ charge and fractional self-statistics $theta_s=frac{pi}{16}$. Finally we argue for an equivalent description via the $d=infty$ limit through topological charge-$4e$ pairing of composite fermions. We suggest graphene double layers should access this phase and propose various experimental signatures, including an Ising transition $T_{Ising}$ below the Berezinskii-Kosterlitz-Thouless transition $T_{BKT}$ at $d sim d_{c1}$.
