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We present post-jet-break \textit{HST}, VLA and \textit{Chandra} observationsof the afterglow of the long $\gamma$-ray bursts GRB 160625B (between 69 and209 days) and GRB 160509A (between 35 and 80 days). We calculate thepost-jet-break decline rates of the light curves, and find the afterglow of GRB160625B inconsistent with a simple $t^{-3/4}$ steepening over the break,expected from the geometric effect of the jet edge entering our line of sight.However, the favored optical post-break decline ($f_{\nu} \propto t^{-1.96 \pm0.07}$) is also inconsistent with the $f_{\nu} \propto t^{-p}$ decline (where$p \approx 2.3$ from the pre-break light curve), which is expected fromexponential lateral expansion of the jet; perhaps suggesting lateral expansionthat only affects a fraction of the jet. The post-break decline of GRB 160509Ais consistent with both the $t^{-3/4}$ steepening and with $f_{\nu} \proptot^{-p}$. We also use {\sc boxfit} to fit afterglow models to both light curvesand find both to be energetically consistent with a millisecond magnetarcentral engine, although the magnetar parameters need to be extreme (i.e. $E\sim 3 \times 10^{52}$ erg). Finally, the late-time radio light curves of bothafterglows are not reproduced well by {\sc boxfit} and are inconsistent withpredictions from the standard jet model; instead both are well represented by asingle power law decline (roughly $f_{\nu} \propto t^{-1}$) with no breaks.This requires a highly chromatic jet break ($t_{j,\mathrm{radio}} > 10 \timest_{j,\mathrm{optical}}$) and possibly a two-component jet for both bursts.

The late-time afterglow evolution of long gamma-ray bursts GRB 160625B and GRB 160509A