There'd be no reason for Shakespeare to burst into Latin at that point unless he was quoting "famous" last words, which he would have got from whatever his source for the history was. The original is Suetonius (always with a caveat that I should rather be saying Tacitus, but I think Suetonius), who says that according to some reports Caesar said kai su, teknon "and you, lad". An Elizabethan theatre audience couldn't be expected to understand Greek, so a switch into Latin would give an equivalent feel. Well that's my theory anyway.