Bookmarks->{"1":>{var1=valInitial, var2=val2,...},"2":>{var1=valFinal,var2=val2,...}},
InterpolationOrder->1

Setting /@ Table[
   With[{aInit = 1.5, tMax = tm},
       Manipulate[Plot[Sin[a t], {t, 0, tMax}], {{a, aInit}, 1, 2}]
   ],
   {tm, 1, 10}
]