From my calculations, if you added 141W of solar capacity and it was 100% efficient (hahaha) then you could keep running during the day.
You could consider a 200W solar panel. They are about 1.5m high and a 1m wide - so a tad tricky to carry - but would give you the ability to operate for quite some time - if the sun remains shining - leaving the batteries for when it was not shining.
A deep cycle "gel" battery is only about 20kg. So not too heavy. The bonus with this is if after 24 hours or so you start to run low just take it out to a vehicle, start it up, put the jumper leads on - and charge it up on the spot. Handy huh?
You could also use a much smaller solar panel (say 100W) with a deep cycle battery and leave it trickle charging all the time. The battery would eventually go flat still (because it sounds like you are using 141W of power) - but it would give you considerable running time.