Another trick you may find handy is to wear a safari vest. You may feel silly in it, but you can stow lenses, and lots of stuff in the pockets, and it isn't considered carry on since you wear it.
I did that too, not a safari vest just a nice big polar fleece, in June, 28 degrees C, flying from Schiphol back to australia via Singapore (31C and 99% humidity). Had about 3-4 lenses and a laptop charger in my jacket, a P&S and wallet and about 1kg of various coins from around the world in my pants pockets, laptop and camera and books in my backpack weighing about 13kg, plus 22kg of checked baggage including a pair of skis. Singapore Airlines officially only give you 20kg still, but I made a comment like, "ah, 1kg under" when I weighed it at the check-in desk, as most airlines these days give you 23kg. Was just lucky that noone weighed my backpack, being an 85kg 6' bloke I wasn't straining too much so they probably never suspected.
It used to be the case that any ticket going through/via the USA you got 30 or 40kg checked baggage, my dad used to fly around the world a lot for work (he was a ship's Captain), the company always sent him on a flight through the US so he could get a lot more baggage, cheaper than a quicker/more direct flight paying excess baggage allowances. So if you're coming from the USA you should get more baggage allowance, that's probably airline-dependent these days though.
+1 on the EasyJet once you get over there, book long enough in advance and pay like $10 a seat, the unlimited-weight-as-long-as-you-can-carry-it-yourself has proven more than useful for me in the past.
Also, I've never flown through Frankfurt, though I've done Schiphol, Heathrow, Gatwick, Stanstead, Luton all often enough that I wouldn't bother. You're probably better off going to Frankfurt for any continent-based travel, then hop on a german ICE fast-train
, book up to 90 days in advance and you can generally get anywhere between NL, Belgium, Germany, Denmark, Poland, Austria, Switzerland for as little as €30, much preferable to flying and take all you can carry (also, you get as much leg-room as business class on a plane).
To go to the UK you can also get to Schiphol, take the Thalys or hourly-Intercity to Brussels, and Eurostar to St Pancras (from my place in The Hague that was quicker to my sister in London (Hammersmith) than bothering with planes). Schiphol as an airport isn't bad, but because of the density of the country I'd only recommend it if your first stop is NL, the german ICEs go through there but they're limited to 150-200km/h until they get to germany, only then they can go 350km/h, so Frankfurt is better for German/Austrian/Swiss travel.