Richard Jones, a vastly experienced woodworker, posted on this subject recently and made a very interesting observation. He said if you apply Teak Oil or other oils to outdoor timber it looks great for a year or two, but once it degrades it looks worse than if you'd never applied anything at all, with a kind of a mildew type look to the timber, then after another three or four years that disappears and you're back to the clean silvery grey look of weathered timber. That exactly matches my observations too.
He hypothesised that products like linseed oil are actually food for microbes, and that's what gives that algae/lichen look to previously oiled timbers. After four or five years all the food is exhausted and you're back to a "clean" timber.
Makes sense to me, and as Richard said I can't think of a better explanation.
So your choice is simple.
1. Do nothing and learn to love weathered timber.
2. Apply an oil but recognise you'll have to sand and re-apply every year or so...for ever!
3. Use a Sikkens type product which is actually paint, albeit a semi transparent, wood coloured paint. Not to everyone's taste but if you like it that's all that counts as you're the one that has to live with it.
Good luck!