big, considerable, dramatic, drastic, enormous, exponential, huge, large, major, marked, massive, significant, substantial, vast
moderate, modest, slight, small
apparent
rapid, sharp, steep, sudden
gradual, incremental, progressive, steady
fivefold, tenfold, etc.
10%, etc.
double-digit (esp. AmE)
Sales of beef have experienced double-digit increases.

concomitant (formal), corresponding, proportional, resulting
Their reputation has improved, bringing a corresponding increase in revenues.

average, mean
The average increase in value last year was 4.3%.

net, overall, total
across-the-board
The pay rise represented an across-the-board increase of between 9% for the highest paid and 32% for the lowest paid worker.

annual, monthly, etc.
projected, proposed
Retirement planning often starts with projected cost-of-living increases.

pay, salary, wage
budget, dividend, fare, price, rent, spending, tax, tuition (AmE)
population, productivity, temperature

demonstrate, experience, see, show
Many parts of the country have experienced an increase in unemployment.
This year saw an increase in the number of job applicants.
Profits show a steady increase.

enjoy
The country is enjoying the biggest increase in business confidence for years.

achieve
We achieved a small increase in profits of £3 257.

bring, bring about, cause, lead to, produce, result in
Intensive farming has brought about an increase in outbreaks of food poisoning.
The war resulted in a massive increase in government spending.

observe
You would expect to observe an increase in births during peacetime.

predict
Some companies are predicting price increases of 30% or more.

propose, suggest
He proposed a large tax increase.

indicate, reflect, represent
Improved profitability may indicate an increase in competitiveness.

be accompanied by, involve, mean
The measures to improve the health service will involve an increase in government spending.

announce, post, report
The company reported a 9.5% increase in third quarter losses.

occur

on the increase
Burglaries in the area are on the increase.

increase in
There has been an increase in demand for two-bedroom houses.

increase on, increase over
The figures show a sharp increase on last year's turnover.

increase to
a dividend increase to 11.4 pence

a rate of increase

considerably, dramatically, drastically, enormously, exponentially, greatly, markedly, significantly, substantially, tremendously, vastly
slightly
gradually, progressively
Progressively increase the intensity of the exercise over three weeks.

rapidly, sharply, steeply
steadily
slowly
twofold, threefold, etc.
Sales increased almost fourfold in this period.

be expected to, be likely to
Demand is expected to increase over the next decade.

by
The budget has increased by more than a third in the last year.

from
in
to increase in amount/number/price/size

to
Last month the reward was increased from $20 000 to $40 000.

with
Disability increases with age.

Increase is used with these nouns as the subject:
amount, appetite, asset, attendance, awareness, catch, circulation, concentration, confidence, consumption, cost, count, crime, deficit, demand, density, discomfort, emission, employment, enrolment, expenditure, expense, export, fare, fee, funding, heat, humidity, import, incidence, income, index, inequality, inflation, investment, length, light, margin, migration, momentum, mortality, noise, number, odds, output, pace, pain, participation, percentage, population, premium, pressure, price, production, productivity, profit, proportion, rate, reliability, rent, return, revenue, salary, sale, scope, size, speed, stature, stock, strength, supply, tax, temperature, tension, tourism, trade, traffic, turnover, unemployment, usage, value, velocity, violence, volume, vote, wage, weight, width, wind, workforce, workload

Increase is used with these nouns as the object:
accountability, accuracy, allocation, amount, angle, anxiety, appeal, appetite, appreciation, asset, attendance, availability, awareness, base, benefit, bid, blood pressure, budget, burden, bureaucracy, capability, capacity, chance, charge, cholesterol, circulation, clarity, clout, competence, competition, complexity, concentration, confidence, congestion, consumption, cooperation, cost, count, credibility, danger, deficit, demand, density, dependence, diameter, difficulty, disparity, diversity, dividend, dosage, dose, duration, duty, earnings, effectiveness, efficiency, effort, employment, endurance, engagement, enjoyment, enrolment, erosion, excise, expenditure, export, exposure, extent, fare, fee, fine, fitness, flexibility, flow, force, frequency, funding, gain, height, hold, humidity, immigration, impact, importance, incentive, incidence, income, inequality, influence, intake, intensity, interest, investment, knowledge, lead, length, level, leverage, likelihood, limit, literacy, majority, manpower, margin, membership, mobility, momentum, mortality, motivation, number, occurrence, odds, offer, output, overdraft, pace, pain, participation, pay, payment, penalty, penetration, pension, per cent, performance, point, pool, potency, potential, power, precision, premium, presence, prestige, price, probability, production, productivity, proficiency, profile, profit, profitability, quota, range, rate, ratio, reach, relevance, reliability, reliance, rent, repertoire, representation, reserve, resilience, return, revenue, risk, role, safety, salary, sale, saving, scale, scope, score, security, self-confidence, setting, severity, share, size, skill, speculation, speed, spending, stability, stake, stamina, stock, strain, strength, stress, subsidy, success, suffering, supply, support, surveillance, tariff, tax, taxation, temperature, tempo, tendency, tension, tolerance, tourism, trade, traffic, tuition, turnout, turnover, uncertainty, understanding, unemployment, unpopularity, urgency, usage, use, usefulness, utility, value, velocity, vigilance, visibility, vitality, vocabulary, voltage, volume, vulnerability, wage, wastage, wealth, width, workforce, workload, worry, worth