weak battery is likely, or a bad ground connection. Possibly a starter problem as well.
with the plugs removed, its relatively easy to crank the engine over. put the plugs in, and the effort increases a LOT. I suspect battery or connection problem, because without the plugs, it the starter wont pull as many amps (battery can supply enough, or the suspect connection is allowing enough amperage to flow). Put the plugs in, and the starter will draw in excess of 200 amps, and the battery and all associated cables and connection need to be top notch to enable that much current to flow properly.